GCSE Maths: Rounding and truncation (Higher)

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping. To round to the nearest whole number we keep the units digit. The digits after the decimal point are only used to decide whether to round up or down.
   3.6
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 6: 6 is 5 or more, so round up.
3. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   3 + 1 = 4
4. Write the rounded answer. Remove the decimal point and everything after it.
   3.6 = 4 (the nearest whole number)

Check. The difference between 3.6 and 4 is 0.4. That is less than or equal to half of 1 (which is 0.5), so 4 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping. To round to the nearest whole number we keep the units digit. The digits after the decimal point are only used to decide whether to round up or down.
   12.3
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 3: 3 is less than 5, so round down (the kept digit does not change).
3. Write the rounded answer. Remove the decimal point and everything after it.
   12.3 = 12 (the nearest whole number)

Check. The difference between 12.3 and 12 is 0.3. That is less than or equal to half of 1 (which is 0.5), so 12 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping. To round to the nearest whole number we keep the units digit. The digits after the decimal point are only used to decide whether to round up or down.
   7.5
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 5: 5 is 5 or more, so round up.
3. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   7 + 1 = 8
4. Write the rounded answer. Remove the decimal point and everything after it.
   7.5 = 8 (the nearest whole number)

Check. The difference between 7.5 and 8 is 0.5. That is less than or equal to half of 1 (which is 0.5), so 8 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping. To round to the nearest whole number we keep the units digit. The digits after the decimal point are only used to decide whether to round up or down.
   0.49
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 4: 4 is less than 5, so round down (the kept digit does not change).
3. Write the rounded answer. Remove the decimal point and everything after it.
   0.49 = 0 (the nearest whole number)

Check. The difference between 0.49 and 0 is 0.49. That is less than or equal to half of 1 (which is 0.5), so 0 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping. To round to the nearest whole number we keep the units digit. The digits after the decimal point are only used to decide whether to round up or down.
   19.5
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 5: 5 is 5 or more, so round up.
3. Round up. The kept digit is 9. Adding 1 gives 10, so we write 0 and carry 1 into the next column to the left.
   19.5 → 20
4. Write the rounded answer. Remove the decimal point and everything after it.
   19.5 = 20 (the nearest whole number)

Check. The difference between 19.5 and 20 is 0.5. That is less than or equal to half of 1 (which is 0.5), so 20 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping. To round to the nearest whole number we keep the units digit. The digits after the decimal point are only used to decide whether to round up or down.
   99.9
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 9: 9 is 5 or more, so round up.
3. Round up. The kept digit is 9. Adding 1 gives 10, so we write 0 and carry 1 into the next column to the left.
   99.9 → 100
4. Write the rounded answer. Remove the decimal point and everything after it.
   99.9 = 100 (the nearest whole number)

Check. The difference between 99.9 and 100 is 0.1. That is less than or equal to half of 1 (which is 0.5), so 100 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the first digit after the decimal point. 1 decimal place means 1 digit after the decimal point. That digit is in the tenths column.
   4.36 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 6: 6 is 5 or more, so round up.
3. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   3 + 1 = 4
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   4.36 = 4.4 (1 decimal place)

Check. The difference between 4.36 and 4.4 is 0.04. That is less than or equal to half of 0.1 (which is 0.05), so 4.4 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the first digit after the decimal point. 1 decimal place means 1 digit after the decimal point. That digit is in the tenths column.
   0.847 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 4: 4 is less than 5, so round down (the kept digit does not change).
3. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.847 = 0.8 (1 decimal place)

Check. The difference between 0.847 and 0.8 is 0.047. That is less than or equal to half of 0.1 (which is 0.05), so 0.8 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the first digit after the decimal point. 1 decimal place means 1 digit after the decimal point. That digit is in the tenths column.
   12.05 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 5: 5 is 5 or more, so round up.
3. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   0 + 1 = 1
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   12.05 = 12.1 (1 decimal place)

Check. The difference between 12.05 and 12.1 is 0.05. That is less than or equal to half of 0.1 (which is 0.05), so 12.1 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the first digit after the decimal point. 1 decimal place means 1 digit after the decimal point. That digit is in the tenths column.
   9.96 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 6: 6 is 5 or more, so round up.
3. Round up. The kept digit is 9. Adding 1 gives 10, so we write 0 and carry 1 into the next column to the left.
   9.96 → 10.0
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   9.96 = 10.0 (1 decimal place)

Check. The difference between 9.96 and 10.0 is 0.04. That is less than or equal to half of 0.1 (which is 0.05), so 10.0 is the closest value with that accuracy. ✓

Watch out. Keep a zero on the end if it is needed: 10.0 has 1 decimal place, and writing it as 10 would show less accuracy.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the first digit after the decimal point. 1 decimal place means 1 digit after the decimal point. That digit is in the tenths column.
   3.449 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 4: 4 is less than 5, so round down (the kept digit does not change).
3. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   3.449 = 3.4 (1 decimal place)

Check. The difference between 3.449 and 3.4 is 0.049. That is less than or equal to half of 0.1 (which is 0.05), so 3.4 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the first digit after the decimal point. 1 decimal place means 1 digit after the decimal point. That digit is in the tenths column.
   0.052 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 5: 5 is 5 or more, so round up.
3. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   0 + 1 = 1
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.052 = 0.1 (1 decimal place)

Check. The difference between 0.052 and 0.1 is 0.048. That is less than or equal to half of 0.1 (which is 0.05), so 0.1 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the second digit after the decimal point. 2 decimal places means 2 digits after the decimal point. That digit is in the hundredths column.
   5.678 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 8: 8 is 5 or more, so round up.
3. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   7 + 1 = 8
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   5.678 = 5.68 (2 decimal places)

Check. The difference between 5.678 and 5.68 is 0.002. That is less than or equal to half of 0.01 (which is 0.005), so 5.68 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the second digit after the decimal point. 2 decimal places means 2 digits after the decimal point. That digit is in the hundredths column.
   0.0942 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 4: 4 is less than 5, so round down (the kept digit does not change).
3. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.0942 = 0.09 (2 decimal places)

Check. The difference between 0.0942 and 0.09 is 0.0042. That is less than or equal to half of 0.01 (which is 0.005), so 0.09 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the second digit after the decimal point. 2 decimal places means 2 digits after the decimal point. That digit is in the hundredths column.
   12.999 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 9: 9 is 5 or more, so round up.
3. Round up. The kept digit is 9. Adding 1 gives 10, so we write 0 and carry 1 into the next column to the left.
   12.999 → 13.00
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   12.999 = 13.00 (2 decimal places)

Check. The difference between 12.999 and 13.00 is 0.001. That is less than or equal to half of 0.01 (which is 0.005), so 13.00 is the closest value with that accuracy. ✓

Watch out. Keep a zero on the end if it is needed: 13.00 has 2 decimal places, and writing it as 13 would show less accuracy.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the second digit after the decimal point. 2 decimal places means 2 digits after the decimal point. That digit is in the hundredths column.
   3.005 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 5: 5 is 5 or more, so round up.
3. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   0 + 1 = 1
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   3.005 = 3.01 (2 decimal places)

Check. The difference between 3.005 and 3.01 is 0.005. That is less than or equal to half of 0.01 (which is 0.005), so 3.01 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the second digit after the decimal point. 2 decimal places means 2 digits after the decimal point. That digit is in the hundredths column.
   7.1349 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 4: 4 is less than 5, so round down (the kept digit does not change).
3. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   7.1349 = 7.13 (2 decimal places)

Check. The difference between 7.1349 and 7.13 is 0.0049. That is less than or equal to half of 0.01 (which is 0.005), so 7.13 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the second digit after the decimal point. 2 decimal places means 2 digits after the decimal point. That digit is in the hundredths column.
   0.396 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 6: 6 is 5 or more, so round up.
3. Round up. The kept digit is 9. Adding 1 gives 10, so we write 0 and carry 1 into the next column to the left.
   0.396 → 0.40
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.396 = 0.40 (2 decimal places)

Check. The difference between 0.396 and 0.40 is 0.004. That is less than or equal to half of 0.01 (which is 0.005), so 0.40 is the closest value with that accuracy. ✓

Watch out. Keep a zero on the end if it is needed: 0.40 has 2 decimal places, and writing it as 0.4 would show less accuracy.

Method. Numbers that round to 5.7 are at least halfway between 5.6 and 5.7.

1. Find the halfway point below 5.7. 5.6 and 5.7 have halfway point 5.65.
   (5.6 + 5.7) ÷ 2 = 5.65
2. Check 5.65 rounds up. The decider is 5, so it rounds up.
   5.65 → 5.7
3. Check the number just below. 5.64 has decider 4.
   5.64 → 5.6, so 5.65 is the smallest.

Check. 5.65 → 5.7 and 5.64 → 5.6. ✓

Method. Numbers that round to 5.7 are below the halfway point between 5.7 and 5.8.

1. Find the halfway point above 5.7. 5.7 and 5.8 have halfway point 5.75.
   5.75
2. 5.75 rounds up to 5.8. The decider is 5, so 5.75 is too big.
   5.75 → 5.8
3. The largest 2 d.p. number below 5.75 is 5.74. 5.74 has decider 4.
   5.74 → 5.7

Check. 5.74 → 5.7 and 5.75 → 5.8. ✓

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 48 is 4, in the tens column.
2. Count 1 significant figure to find the last digit you are keeping. The first significant figure is number 1. The digit number 1 is in the tens column.
   48 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 8: 8 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   4 + 1 = 5
5. Write the rounded answer. Digits before the decimal point cannot be removed, or the number would become much smaller. Replace them with zeros (placeholder zeros).
   48 = 50 (1 significant figure)

Check. The difference between 48 and 50 is 2. That is less than or equal to half of 10 (which is 5), so 50 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 0.0762 is 7, in the hundredths column.
2. Count 1 significant figure to find the last digit you are keeping. The first significant figure is number 1. The digit number 1 is in the hundredths column.
   0.0762 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 6: 6 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   7 + 1 = 8
5. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.0762 = 0.08 (1 significant figure)

Check. The difference between 0.0762 and 0.08 is 0.0038. That is less than or equal to half of 0.01 (which is 0.005), so 0.08 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 5921 is 5, in the thousands column.
2. Count 1 significant figure to find the last digit you are keeping. The first significant figure is number 1. The digit number 1 is in the thousands column.
   5921 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 9: 9 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   5 + 1 = 6
5. Write the rounded answer. Digits before the decimal point cannot be removed, or the number would become much smaller. Replace them with zeros (placeholder zeros).
   5921 = 6000 (1 significant figure)

Check. The difference between 5921 and 6000 is 79. That is less than or equal to half of 1000 (which is 500), so 6000 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 0.00349 is 3, in the thousandths column.
2. Count 1 significant figure to find the last digit you are keeping. The first significant figure is number 1. The digit number 1 is in the thousandths column.
   0.00349 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 4: 4 is less than 5, so round down (the kept digit does not change).
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.00349 = 0.003 (1 significant figure)

Check. The difference between 0.00349 and 0.003 is 0.00049. That is less than or equal to half of 0.001 (which is 0.0005), so 0.003 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 3.96 is 3, in the units column.
2. Count 1 significant figure to find the last digit you are keeping. The first significant figure is number 1. The digit number 1 is in the units column.
   3.96 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 9: 9 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   3 + 1 = 4
5. Write the rounded answer. Remove the decimal point and everything after it.
   3.96 = 4 (1 significant figure)

Check. The difference between 3.96 and 4 is 0.04. That is less than or equal to half of 1 (which is 0.5), so 4 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 95 is 9, in the tens column.
2. Count 1 significant figure to find the last digit you are keeping. The first significant figure is number 1. The digit number 1 is in the tens column.
   95 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 5: 5 is 5 or more, so round up.
4. Round up. The kept digit is 9. Adding 1 gives 10, so we write 0 and carry 1 into the next column to the left.
   95 → 100
5. Write the rounded answer. Digits before the decimal point cannot be removed, or the number would become much smaller. Replace them with zeros (placeholder zeros).
   95 = 100 (1 significant figure)

Check. The difference between 95 and 100 is 5. That is less than or equal to half of 10 (which is 5), so 100 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 3.482 is 3, in the units column.
2. Count 2 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 2 is in the tenths column.
   3.482 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 8: 8 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   4 + 1 = 5
5. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   3.482 = 3.5 (2 significant figures)

Check. The difference between 3.482 and 3.5 is 0.018. That is less than or equal to half of 0.1 (which is 0.05), so 3.5 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 0.05269 is 5, in the hundredths column.
2. Count 2 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 2 is in the thousandths column.
   0.05269 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 6: 6 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   2 + 1 = 3
5. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.05269 = 0.053 (2 significant figures)

Check. The difference between 0.05269 and 0.053 is 0.00031. That is less than or equal to half of 0.001 (which is 0.0005), so 0.053 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 7619 is 7, in the thousands column.
2. Count 2 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 2 is in the hundreds column.
   7619 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 1: 1 is less than 5, so round down (the kept digit does not change).
4. Write the rounded answer. Digits before the decimal point cannot be removed, or the number would become much smaller. Replace them with zeros (placeholder zeros).
   7619 = 7600 (2 significant figures)

Check. The difference between 7619 and 7600 is 19. That is less than or equal to half of 100 (which is 50), so 7600 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 12.96 is 1, in the tens column.
2. Count 2 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 2 is in the units column.
   12.96 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 9: 9 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   2 + 1 = 3
5. Write the rounded answer. Remove the decimal point and everything after it.
   12.96 = 13 (2 significant figures)

Check. The difference between 12.96 and 13 is 0.04. That is less than or equal to half of 1 (which is 0.5), so 13 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 0.003051 is 3, in the thousandths column.
2. Count 2 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 2 is in the ten-thousandths column.
   0.003051 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 5: 5 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   0 + 1 = 1
5. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.003051 = 0.0031 (2 significant figures)

Check. The difference between 0.003051 and 0.0031 is 0.000049. That is less than or equal to half of 0.0001 (which is 0.00005), so 0.0031 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 450.7 is 4, in the hundreds column.
2. Count 2 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 2 is in the tens column.
   450.7 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 0: 0 is less than 5, so round down (the kept digit does not change).
4. Write the rounded answer. Digits before the decimal point cannot be removed, or the number would become much smaller. Replace them with zeros (placeholder zeros).
   450.7 = 450 (2 significant figures)

Check. The difference between 450.7 and 450 is 0.7. That is less than or equal to half of 10 (which is 5), so 450 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 4.5678 is 4, in the units column.
2. Count 3 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 3 is in the hundredths column.
   4.5678 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 7: 7 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   6 + 1 = 7
5. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   4.5678 = 4.57 (3 significant figures)

Check. The difference between 4.5678 and 4.57 is 0.0022. That is less than or equal to half of 0.01 (which is 0.005), so 4.57 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 0.0123456 is 1, in the hundredths column.
2. Count 3 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 3 is in the ten-thousandths column.
   0.0123456 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 4: 4 is less than 5, so round down (the kept digit does not change).
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.0123456 = 0.0123 (3 significant figures)

Check. The difference between 0.0123456 and 0.0123 is 0.0000456. That is less than or equal to half of 0.0001 (which is 0.00005), so 0.0123 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 56 789 is 5, in the ten thousands column.
2. Count 3 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 3 is in the hundreds column.
   56789 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 8: 8 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   7 + 1 = 8
5. Write the rounded answer. Digits before the decimal point cannot be removed, or the number would become much smaller. Replace them with zeros (placeholder zeros).
   56 789 = 56 800 (3 significant figures)

Check. The difference between 56 789 and 56 800 is 11. That is less than or equal to half of 100 (which is 50), so 56 800 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 2.998 is 2, in the units column.
2. Count 3 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 3 is in the hundredths column.
   2.998 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 8: 8 is 5 or more, so round up.
4. Round up. The kept digit is 9. Adding 1 gives 10, so we write 0 and carry 1 into the next column to the left.
   2.998 → 3.00
5. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   2.998 = 3.00 (3 significant figures)

Check. The difference between 2.998 and 3.00 is 0.002. That is less than or equal to half of 0.01 (which is 0.005), so 3.00 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 0.80049 is 8, in the tenths column.
2. Count 3 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 3 is in the thousandths column.
   0.80049 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 4: 4 is less than 5, so round down (the kept digit does not change).
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   0.80049 = 0.800 (3 significant figures)

Check. The difference between 0.80049 and 0.800 is 0.00049. That is less than or equal to half of 0.001 (which is 0.0005), so 0.800 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 1234.5 is 1, in the thousands column.
2. Count 3 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 3 is in the tens column.
   1234.5 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 4: 4 is less than 5, so round down (the kept digit does not change).
4. Write the rounded answer. Digits before the decimal point cannot be removed, or the number would become much smaller. Replace them with zeros (placeholder zeros).
   1234.5 = 1230 (3 significant figures)

Check. The difference between 1234.5 and 1230 is 4.5. That is less than or equal to half of 10 (which is 5), so 1230 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. To truncate a number is to cut it off after a given digit, without looking at the next digit.

Method. To truncate, keep the digits up to the place you are told and cut off everything after it, without rounding.

1. Find the last digit you are keeping. 1 decimal place means 1 digit after the decimal point, in the tenths column.
   4.78 (blue = last digit kept)
2. Cut off every digit after it. Do not look at the next digit and do not round up. Truncating means chopping the number off at that point, even if the next digit is large.
   4.78: everything after the blue digit is removed
3. Write the truncated number. Keep the digits up to the last one you kept.
   4.78 truncated = 4.7

Check. A truncated number is never bigger than the original, and the difference is less than one unit of the last column: 0.08 < 0.1. ✓
If we had rounded instead, we would have got 4.8.

Watch out. Truncating is not the same as rounding. 3.79 truncated to 1 decimal place is 3.7, but rounded it is 3.8.

Key words. To truncate a number is to cut it off after a given digit, without looking at the next digit.

Method. To truncate, keep the digits up to the place you are told and cut off everything after it, without rounding.

1. Find the last digit you are keeping. 2 decimal places means 2 digits after the decimal point, in the hundredths column.
   12.999 (blue = last digit kept)
2. Cut off every digit after it. Do not look at the next digit and do not round up. Truncating means chopping the number off at that point, even if the next digit is large.
   12.999: everything after the blue digit is removed
3. Write the truncated number. Keep the digits up to the last one you kept.
   12.999 truncated = 12.99

Check. A truncated number is never bigger than the original, and the difference is less than one unit of the last column: 0.009 < 0.01. ✓
If we had rounded instead, we would have got 13.00.

Watch out. Truncating is not the same as rounding. 3.79 truncated to 1 decimal place is 3.7, but rounded it is 3.8.

Key words. To truncate a number is to cut it off after a given digit, without looking at the next digit.

Method. To truncate, keep the digits up to the place you are told and cut off everything after it, without rounding.

1. Count 2 significant figures from the first non-zero digit. Zeros at the start do not count. The last digit you count is the last one you keep.
   0.0567 (blue = last digit kept)
2. Cut off every digit after it. Do not look at the next digit and do not round up. Truncating means chopping the number off at that point, even if the next digit is large.
   0.0567: everything after the blue digit is removed
3. Write the truncated number. Keep the digits up to the last one you kept.
   0.0567 truncated = 0.056

Check. A truncated number is never bigger than the original, and the difference is less than one unit of the last column: 0.0007 < 0.001. ✓
If we had rounded instead, we would have got 0.057.

Watch out. Truncating is not the same as rounding. 3.79 truncated to 1 decimal place is 3.7, but rounded it is 3.8.

Key words. To truncate a number is to cut it off after a given digit, without looking at the next digit.

Method. To truncate, keep the digits up to the place you are told and cut off everything after it, without rounding.

1. Count 2 significant figures from the first non-zero digit. Zeros at the start do not count. The last digit you count is the last one you keep.
   4567 (blue = last digit kept)
2. Cut off every digit after it. Do not look at the next digit and do not round up. Truncating means chopping the number off at that point, even if the next digit is large.
   4567: everything after the blue digit is removed
3. Write the truncated number. Keep the digits up to the last one you kept. Digits before the decimal point that were cut off are replaced by zeros, to keep the number the right size.
   4567 truncated = 4500

Check. A truncated number is never bigger than the original, and the difference is less than one unit of the last column: 67 < 100. ✓
If we had rounded instead, we would have got 4600.

Watch out. Truncating is not the same as rounding. 3.79 truncated to 1 decimal place is 3.7, but rounded it is 3.8.

Key words. To truncate a number is to cut it off after a given digit, without looking at the next digit.

Method. To truncate, keep the digits up to the place you are told and cut off everything after it, without rounding.

1. Find the last digit you are keeping. 1 decimal place means 1 digit after the decimal point, in the tenths column.
   9.99 (blue = last digit kept)
2. Cut off every digit after it. Do not look at the next digit and do not round up. Truncating means chopping the number off at that point, even if the next digit is large.
   9.99: everything after the blue digit is removed
3. Write the truncated number. Keep the digits up to the last one you kept.
   9.99 truncated = 9.9

Check. A truncated number is never bigger than the original, and the difference is less than one unit of the last column: 0.09 < 0.1. ✓
If we had rounded instead, we would have got 10.0.

Watch out. Truncating is not the same as rounding. 3.79 truncated to 1 decimal place is 3.7, but rounded it is 3.8.

Key words. To truncate a number is to cut it off after a given digit, without looking at the next digit.

Method. To truncate, keep the digits up to the place you are told and cut off everything after it, without rounding.

1. Find the last digit you are keeping. 0 decimal places means 0 digits after the decimal point, in the units column.
   0.8 (blue = last digit kept)
2. Cut off every digit after it. Do not look at the next digit and do not round up. Truncating means chopping the number off at that point, even if the next digit is large.
   0.8: everything after the blue digit is removed
3. Write the truncated number. Keep the digits up to the last one you kept.
   0.8 truncated = 0

Check. A truncated number is never bigger than the original, and the difference is less than one unit of the last column: 0.8 < 1. ✓
If we had rounded instead, we would have got 1.

Watch out. Truncating is not the same as rounding. 3.79 truncated to 1 decimal place is 3.7, but rounded it is 3.8.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the second digit after the decimal point. 2 decimal places means 2 digits after the decimal point. That digit is in the hundredths column.
   8.746 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 6: 6 is 5 or more, so round up.
3. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   4 + 1 = 5
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   8.746 = 8.75 (2 decimal places)

Check. The difference between 8.746 and 8.75 is 0.004. That is less than or equal to half of 0.01 (which is 0.005), so 8.75 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. To truncate a number is to cut it off after a given digit, without looking at the next digit.

Method. To truncate, keep the digits up to the place you are told and cut off everything after it, without rounding.

1. Find the last digit you are keeping. 2 decimal places means 2 digits after the decimal point, in the hundredths column.
   8.746 (blue = last digit kept)
2. Cut off every digit after it. Do not look at the next digit and do not round up. Truncating means chopping the number off at that point, even if the next digit is large.
   8.746: everything after the blue digit is removed
3. Write the truncated number. Keep the digits up to the last one you kept.
   8.746 truncated = 8.74

Check. A truncated number is never bigger than the original, and the difference is less than one unit of the last column: 0.006 < 0.01. ✓
If we had rounded instead, we would have got 8.75.

Watch out. Truncating is not the same as rounding. 3.79 truncated to 1 decimal place is 3.7, but rounded it is 3.8.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the digit in the thousands column. This is the last digit you are keeping. Rounding to the nearest thousand means the answer ends in the thousands column.
   24683 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 6: 6 is 5 or more, so round up.
3. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   4 + 1 = 5
4. Write the rounded answer. Digits before the decimal point cannot be removed, or the number would become much smaller. Replace them with zeros (placeholder zeros).
   24 683 = 25 000 (the nearest thousand)

Check. The difference between 24 683 and 25 000 is 317. That is less than or equal to half of 1000 (which is 500), so 25 000 is the closest value with that accuracy. ✓

Watch out. Your answer must end with the right number of zeros: 45 678 to the nearest thousand is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 24 683 is 2, in the ten thousands column.
2. Count 2 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 2 is in the thousands column.
   24683 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 6: 6 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   4 + 1 = 5
5. Write the rounded answer. Digits before the decimal point cannot be removed, or the number would become much smaller. Replace them with zeros (placeholder zeros).
   24 683 = 25 000 (2 significant figures)

Check. The difference between 24 683 and 25 000 is 317. That is less than or equal to half of 1000 (which is 500), so 25 000 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 3.14159265 is 3, in the units column.
2. Count 3 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 3 is in the hundredths column.
   3.14159265 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 1: 1 is less than 5, so round down (the kept digit does not change).
4. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   3.14159265 = 3.14 (3 significant figures)

Check. The difference between 3.14159265 and 3.14 is 0.00159265. That is less than or equal to half of 0.01 (which is 0.005), so 3.14 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the last digit you are keeping: the second digit after the decimal point. 2 decimal places means 2 digits after the decimal point. That digit is in the hundredths column.
   3.14159265 (blue = last digit kept)
2. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 1: 1 is less than 5, so round down (the kept digit does not change).
3. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   3.14159265 = 3.14 (2 decimal places)

Check. The difference between 3.14159265 and 3.14 is 0.00159265. That is less than or equal to half of 0.01 (which is 0.005), so 3.14 is the closest value with that accuracy. ✓

Watch out. Look at only the one digit right after the last digit you keep, and do not round twice.

Key words. A decimal place (d.p.) is a digit after the decimal point. A significant figure (s.f.) is a digit that counts towards accuracy, starting from the first non-zero digit. The decider is the digit just after the one you are keeping.

Method. To round, find the last digit you want to keep, look at the next digit (the decider), and round up if it is 5 or more.

1. Find the first significant figure. Significant figures are counted from the first digit that is not zero. Zeros at the start of a decimal do not count, because they only hold the place.
   The first non-zero digit of 3.14159265 is 3, in the units column.
2. Count 5 significant figures to find the last digit you are keeping. The first significant figure is number 1. The digit number 5 is in the ten-thousandths column.
   3.14159265 (blue = last digit kept)
3. Look at the next digit to the right: the decider. If the decider is 5 or more, round up. If it is 4 or less, round down (the last digit stays the same).
   The decider is 9: 9 is 5 or more, so round up.
4. Round up: add 1 to the last digit you are keeping. Rounding up makes the last kept digit one bigger.
   5 + 1 = 6
5. Write the rounded answer. Remove all the digits after the last digit you kept. Keep any zeros that are at the end, because they show how accurate the answer is.
   3.14159265 = 3.1416 (5 significant figures)

Check. The difference between 3.14159265 and 3.1416 is 0.00000735. That is less than or equal to half of 0.0001 (which is 0.00005), so 3.1416 is the closest value with that accuracy. ✓

Watch out. Do not count the zeros at the start of a decimal as significant figures, and put in placeholder zeros for large numbers: 45 678 to 2 s.f. is 46 000, not 46.