Year 4: Comparing, ordering and rounding decimals
Part of the Year 4 tenths, hundredths and money chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Comparing, ordering and rounding decimals
To compare two decimals, write them in a place-value table with the decimal points lined up. Then compare the digits from the left. The first column where the digits are different tells you which number is bigger.
| ones | tenths | hundredths | ||
|---|---|---|---|---|
| 5.34 | 5 | . | 3 | 4 |
| 5.39 | 5 | . | 3 | 9 |
| ones | tenths | ||
|---|---|---|---|
| 4.8 | 4 | . | 8 |
| 4.3 | 4 | . | 3 |
A picture helps. Look at 0.45 and 0.54. The first has 4 full rows and 5 squares. The second has 5 full rows and 4 squares. 5 tenths is more than 4 tenths, so 0.54 is bigger.
0.45
0.54
Ordering means putting numbers in a list. Compare the ones, then the tenths, then the hundredths. For example, to order 0.82, 0.28, 0.88 and 0.08 from smallest to biggest: all have 0 ones. The tenths digits are 8, 2, 8 and 0. So 0.08 is the smallest, then 0.28. The other two both have 8 tenths, so compare hundredths: 0.82 < 0.88. The order is 0.08, 0.28, 0.82, 0.88.
Rounding to the nearest whole number. Look at 3.4. It is between 3 and 4. On a number line, 3.4 is closer to 3.
The halfway point between 3 and 4 is 3.5. Numbers below 3.5 are closer to 3. Numbers from 3.5 up are closer to 4 (halfway, 3.5, rounds up).
The quick rule: look at the tenths digit (the first digit after the point). If it is 5 or more, round up to the next whole number. If it is 4 or less, round down (keep the whole number).
Key words. To compare is to say which is bigger. To order is to put in a list. To round is to change to a nearby number that is easier to use.
Key ideas
- Line up the decimal points and compare the digits from the left.
- The first column where the digits are different decides which number is bigger.
- Order: compare ones, then tenths, then hundredths. List all the numbers.
- Rounding to the nearest whole number: look at the tenths digit.
- 5 or more: round up. 4 or less: round down.
- Halfway (like 3.5) rounds up.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths 4.8 4 . 8 4.3 4 . 3 - Compare the digits from the left. The first column where the digits are different decides.ones: 4 and 4 are the same, so look at the next column.
tenths: 8 and 3 are different. 8 > 3, so 4.8 is bigger. - Write the answer. < means “is less than” and > means “is greater than”.4.8 > 4.3
Check. Picture a number line: 4.3 is to the left of 4.8. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 5.34 5 . 3 4 5.39 5 . 3 9 - Compare the digits from the left. The first column where the digits are different decides.ones: 5 and 5 are the same, so look at the next column.
tenths: 3 and 3 are the same, so look at the next column.
hundredths: 4 and 9 are different. 4 < 9, so 5.34 is smaller. - Write the answer. < means “is less than” and > means “is greater than”.5.34 < 5.39
Check. Picture a number line: 5.34 is to the left of 5.39. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 2.45 2 . 4 5 3.12 3 . 1 2 - Compare the digits from the left. The first column where the digits are different decides.ones: 2 and 3 are different. 2 < 3, so 2.45 is smaller.
- Write the answer. < means “is less than” and > means “is greater than”.2.45 < 3.12
Check. Picture a number line: 2.45 is to the left of 3.12. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them smallest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths hundredths 0.82 0 . 8 2 0.28 0 . 2 8 0.88 0 . 8 8 0.08 0 . 0 8 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 0.82 has 0, 0.28 has 0, 0.88 has 0, 0.08 has 0. All the same, so look at the next column.
Tenths: 0.82 has 8, 0.28 has 2, 0.88 has 8, 0.08 has 0. Smallest to biggest: 0, 2, 8.
Hundredths: 0.82 has 2, 0.88 has 8. Smallest to biggest: 2, 8. - Write them smallest first. Write the ORIGINAL numbers and check that you have used every one.0.08, 0.28, 0.82, 0.88
Check. Count them: 4 numbers in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them biggest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths 3.6 3 . 6 3.1 3 . 1 2.9 2 . 9 3.0 3 . 0 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 3.6 has 3, 3.1 has 3, 2.9 has 2, 3.0 has 3. Smallest to biggest: 2, 3.
Tenths: 3.6 has 6, 3.1 has 1, 3.0 has 0. Smallest to biggest: 0, 1, 6. - Write them biggest first. Write the ORIGINAL numbers and check that you have used every one.3.6, 3.1, 3.0, 2.9
Check. Count them: 4 numbers in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 4.3 is between. Rounding to the nearest whole number means choosing the closest whole number.4 < 4.3 < 5
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 3.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)3 is 4 or less, so round down.
- Look at the number line. The orange dot is 4.3. The green ring is the nearest whole number.
- Write the answer. 4.3 ≈ 4 (to the nearest whole number)
Check. Distances: 4.3 − 4 = 0.3 and 5 − 4.3 = 0.7. 4 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 7.6 is between. Rounding to the nearest whole number means choosing the closest whole number.7 < 7.6 < 8
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 6.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)6 is 5 or more, so round up.
- Look at the number line. The orange dot is 7.6. The green ring is the nearest whole number.
- Write the answer. 7.6 ≈ 8 (to the nearest whole number)
Check. Distances: 7.6 − 7 = 0.6 and 8 − 7.6 = 0.4. 8 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 5.5 is between. Rounding to the nearest whole number means choosing the closest whole number.5 < 5.5 < 6
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 5.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)5 is 5 or more, so round up.
- Look at the number line. The orange dot is 5.5. The green ring is the nearest whole number.
- Write the answer. 5.5 ≈ 6 (to the nearest whole number)
Check. Distances: 5.5 − 5 = 0.5 and 6 − 5.5 = 0.5. 6 is the one we choose when exactly halfway. ✓
Watch out. Exactly halfway (like 6.5) always rounds UP.
Watch out
More digits does not mean a bigger number. 0.45 is smaller than 0.5 even though 45 is bigger than 5. Write 0.5 as 0.50 and compare 45 hundredths with 50 hundredths. And when you round, only look at the tenths digit: 4.49 would round down because the tenths digit is 4.Exercise 6E Comparing, ordering and rounding decimals
Non-calculator0.4
0.7
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths 0.4 0 . 4 0.7 0 . 7 - Compare the digits from the left. The first column where the digits are different decides.ones: 0 and 0 are the same, so look at the next column.
tenths: 4 and 7 are different. 4 < 7, so 0.4 is smaller. - Write the answer. < means “is less than” and > means “is greater than”.0.4 < 0.7
Check. Picture a number line: 0.4 is to the left of 0.7. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
0.35
0.53
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 0.35 0 . 3 5 0.53 0 . 5 3 - Compare the digits from the left. The first column where the digits are different decides.ones: 0 and 0 are the same, so look at the next column.
tenths: 3 and 5 are different. 3 < 5, so 0.35 is smaller. - Write the answer. < means “is less than” and > means “is greater than”.0.35 < 0.53
Check. Picture a number line: 0.35 is to the left of 0.53. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
0.8
0.08
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value (0.5 = 0.50).0.8 = 0.80 and 0.08 = 0.08
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 0.80 0 . 8 0 0.08 0 . 0 8 - Compare the digits from the left. The first column where the digits are different decides.ones: 0 and 0 are the same, so look at the next column.
tenths: 8 and 0 are different. 8 > 0, so 0.80 is bigger. - Write the answer. < means “is less than” and > means “is greater than”.0.8 > 0.08
Check. Picture a number line: 0.08 is to the left of 0.8. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths 0.3 0 . 3 0.8 0 . 8 - Compare the digits from the left. The first column where the digits are different decides.ones: 0 and 0 are the same, so look at the next column.
tenths: 3 and 8 are different. 3 < 8, so 0.3 is smaller. - Write the answer. < means “is less than” and > means “is greater than”.0.3 < 0.8
Check. Picture a number line: 0.3 is to the left of 0.8. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths 2.5 2 . 5 2.1 2 . 1 - Compare the digits from the left. The first column where the digits are different decides.ones: 2 and 2 are the same, so look at the next column.
tenths: 5 and 1 are different. 5 > 1, so 2.5 is bigger. - Write the answer. < means “is less than” and > means “is greater than”.2.5 > 2.1
Check. Picture a number line: 2.1 is to the left of 2.5. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths 4.0 4 . 0 3.9 3 . 9 - Compare the digits from the left. The first column where the digits are different decides.ones: 4 and 3 are different. 4 > 3, so 4.0 is bigger.
- Write the answer. < means “is less than” and > means “is greater than”.4.0 > 3.9
Check. Picture a number line: 3.9 is to the left of 4.0. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths 6.7 6 . 7 6.9 6 . 9 - Compare the digits from the left. The first column where the digits are different decides.ones: 6 and 6 are the same, so look at the next column.
tenths: 7 and 9 are different. 7 < 9, so 6.7 is smaller. - Write the answer. < means “is less than” and > means “is greater than”.6.7 < 6.9
Check. Picture a number line: 6.7 is to the left of 6.9. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths 9.1 9 . 1 8.9 8 . 9 - Compare the digits from the left. The first column where the digits are different decides.ones: 9 and 8 are different. 9 > 8, so 9.1 is bigger.
- Write the answer. < means “is less than” and > means “is greater than”.9.1 > 8.9
Check. Picture a number line: 8.9 is to the left of 9.1. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths 3.3 3 . 3 3.3 3 . 3 - Compare the digits from the left. The first column where the digits are different decides.ones: 3 and 3 are the same, so look at the next column.
tenths: 3 and 3 are the same. Every column is the same, so the numbers are equal. - Write the answer. < means “is less than” and > means “is greater than”.3.3 = 3.3
Check. Both numbers are worth the same. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 0.34 0 . 3 4 0.43 0 . 4 3 - Compare the digits from the left. The first column where the digits are different decides.ones: 0 and 0 are the same, so look at the next column.
tenths: 3 and 4 are different. 3 < 4, so 0.34 is smaller. - Write the answer. < means “is less than” and > means “is greater than”.0.34 < 0.43
Check. Picture a number line: 0.34 is to the left of 0.43. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 5.62 5 . 6 2 5.26 5 . 2 6 - Compare the digits from the left. The first column where the digits are different decides.ones: 5 and 5 are the same, so look at the next column.
tenths: 6 and 2 are different. 6 > 2, so 5.62 is bigger. - Write the answer. < means “is less than” and > means “is greater than”.5.62 > 5.26
Check. Picture a number line: 5.26 is to the left of 5.62. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 1.07 1 . 0 7 1.70 1 . 7 0 - Compare the digits from the left. The first column where the digits are different decides.ones: 1 and 1 are the same, so look at the next column.
tenths: 0 and 7 are different. 0 < 7, so 1.07 is smaller. - Write the answer. < means “is less than” and > means “is greater than”.1.07 < 1.70
Check. Picture a number line: 1.07 is to the left of 1.70. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 3.45 3 . 4 5 3.45 3 . 4 5 - Compare the digits from the left. The first column where the digits are different decides.ones: 3 and 3 are the same, so look at the next column.
tenths: 4 and 4 are the same, so look at the next column.
hundredths: 5 and 5 are the same. Every column is the same, so the numbers are equal. - Write the answer. < means “is less than” and > means “is greater than”.3.45 = 3.45
Check. Both numbers are worth the same. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 0.58 0 . 5 8 0.59 0 . 5 9 - Compare the digits from the left. The first column where the digits are different decides.ones: 0 and 0 are the same, so look at the next column.
tenths: 5 and 5 are the same, so look at the next column.
hundredths: 8 and 9 are different. 8 < 9, so 0.58 is smaller. - Write the answer. < means “is less than” and > means “is greater than”.0.58 < 0.59
Check. Picture a number line: 0.58 is to the left of 0.59. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write the numbers in a place-value table. Compare the digits from the left. The first column where they are different decides which number is bigger.
- Write both numbers in a place-value table. Line up the decimal points so each digit is above a digit of the same value.
ones tenths hundredths 7.91 7 . 9 1 7.19 7 . 1 9 - Compare the digits from the left. The first column where the digits are different decides.ones: 7 and 7 are the same, so look at the next column.
tenths: 9 and 1 are different. 9 > 1, so 7.91 is bigger. - Write the answer. < means “is less than” and > means “is greater than”.7.91 > 7.19
Check. Picture a number line: 7.19 is to the left of 7.91. ✓
Watch out. Start at the LEFT, with the biggest column. And do not count the digits: 0.45 is smaller than 0.5, even though 45 is bigger than 5.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them smallest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths 0.6 0 . 6 0.2 0 . 2 0.9 0 . 9 0.4 0 . 4 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 0.6 has 0, 0.2 has 0, 0.9 has 0, 0.4 has 0. All the same, so look at the next column.
Tenths: 0.6 has 6, 0.2 has 2, 0.9 has 9, 0.4 has 4. Smallest to biggest: 2, 4, 6, 9. - Write them smallest first. Write the ORIGINAL numbers and check that you have used every one.0.2, 0.4, 0.6, 0.9
Check. Count them: 4 numbers in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them smallest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths 3.7 3 . 7 3.1 3 . 1 2.8 2 . 8 3.0 3 . 0 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 3.7 has 3, 3.1 has 3, 2.8 has 2, 3.0 has 3. Smallest to biggest: 2, 3.
Tenths: 3.7 has 7, 3.1 has 1, 3.0 has 0. Smallest to biggest: 0, 1, 7. - Write them smallest first. Write the ORIGINAL numbers and check that you have used every one.2.8, 3.0, 3.1, 3.7
Check. Count them: 4 numbers in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them smallest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths hundredths 0.45 0 . 4 5 0.54 0 . 5 4 0.04 0 . 0 4 0.40 0 . 4 0 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 0.45 has 0, 0.54 has 0, 0.04 has 0, 0.40 has 0. All the same, so look at the next column.
Tenths: 0.45 has 4, 0.54 has 5, 0.04 has 0, 0.40 has 4. Smallest to biggest: 0, 4, 5.
Hundredths: 0.45 has 5, 0.40 has 0. Smallest to biggest: 0, 5. - Write them smallest first. Write the ORIGINAL numbers and check that you have used every one.0.04, 0.40, 0.45, 0.54
Check. Count them: 4 numbers in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them biggest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths 1.5 1 . 5 5.1 5 . 1 1.1 1 . 1 5.5 5 . 5 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 1.5 has 1, 5.1 has 5, 1.1 has 1, 5.5 has 5. Smallest to biggest: 1, 5.
Tenths: 1.5 has 5, 1.1 has 1. Smallest to biggest: 1, 5.
Tenths: 5.1 has 1, 5.5 has 5. Smallest to biggest: 1, 5. - Write them biggest first. Write the ORIGINAL numbers and check that you have used every one.5.5, 5.1, 1.5, 1.1
Check. Count them: 4 numbers in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them biggest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths hundredths 0.72 0 . 7 2 0.27 0 . 2 7 0.77 0 . 7 7 0.07 0 . 0 7 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 0.72 has 0, 0.27 has 0, 0.77 has 0, 0.07 has 0. All the same, so look at the next column.
Tenths: 0.72 has 7, 0.27 has 2, 0.77 has 7, 0.07 has 0. Smallest to biggest: 0, 2, 7.
Hundredths: 0.72 has 2, 0.77 has 7. Smallest to biggest: 2, 7. - Write them biggest first. Write the ORIGINAL numbers and check that you have used every one.0.77, 0.72, 0.27, 0.07
Check. Count them: 4 numbers in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.
Method. Work out what one gap is worth. Then count on from the left end.
- Find the two numbers at the ends and count the gaps. All the gaps on a number line are the same size.The line goes from 5 to 6 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.1 ÷ 10 = 0.1
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 7 gaps after 5.
- Work out the number. Start at the left end and add the gaps.5 + 7 × 0.1 = 5 + 0.7 = 5.7
Check. Count back from 6: 3 gaps back is 6 − 0.3 = 5.7. ✓
Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.
Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.
Method. Work out what one gap is worth. Then count on from the left end.
- Find the two numbers at the ends and count the gaps. All the gaps on a number line are the same size.The line goes from 5 to 6 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.1 ÷ 10 = 0.1
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 2 gaps after 5.
- Work out the number. Start at the left end and add the gaps.5 + 2 × 0.1 = 5 + 0.2 = 5.2
Check. Count back from 6: 8 gaps back is 6 − 0.8 = 5.2. ✓
Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.
Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.
Method. Work out what one gap is worth. Then count on from the left end.
- Find the two numbers at the ends and count the gaps. All the gaps on a number line are the same size.The line goes from 5 to 6 in 10 equal gaps.
- Work out what one gap is worth. Share the distance between the ends equally.1 ÷ 10 = 0.1
- Count the gaps from the left end to the point. Count the gaps, not the tick marks.The point is 9 gaps after 5.
- Work out the number. Start at the left end and add the gaps.5 + 9 × 0.1 = 5 + 0.9 = 5.9
Check. Count back from 6: 1 gap back is 6 − 0.1 = 5.9. ✓
Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them smallest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths 5.7 5 . 7 5.2 5 . 2 5.9 5 . 9 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 5.7 has 5, 5.2 has 5, 5.9 has 5. All the same, so look at the next column.
Tenths: 5.7 has 7, 5.2 has 2, 5.9 has 9. Smallest to biggest: 2, 7, 9. - Write them smallest first. Write the ORIGINAL numbers and check that you have used every one.5.2, 5.7, 5.9
Check. Count them: 3 numbers in the question and 3 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 3.4 is between. Rounding to the nearest whole number means choosing the closest whole number.3 < 3.4 < 4
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 4.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)4 is 4 or less, so round down.
- Write the answer. 3.4 ≈ 3 (to the nearest whole number)
Check. Distances: 3.4 − 3 = 0.4 and 4 − 3.4 = 0.6. 3 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 6.5 is between. Rounding to the nearest whole number means choosing the closest whole number.6 < 6.5 < 7
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 5.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)5 is 5 or more, so round up.
- Write the answer. 6.5 ≈ 7 (to the nearest whole number)
Check. Distances: 6.5 − 6 = 0.5 and 7 − 6.5 = 0.5. 7 is the one we choose when exactly halfway. ✓
Watch out. Exactly halfway (like 6.5) always rounds UP.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 8.9 is between. Rounding to the nearest whole number means choosing the closest whole number.8 < 8.9 < 9
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 9.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)9 is 5 or more, so round up.
- Write the answer. 8.9 ≈ 9 (to the nearest whole number)
Check. Distances: 8.9 − 8 = 0.9 and 9 − 8.9 = 0.1. 9 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 12.1 is between. Rounding to the nearest whole number means choosing the closest whole number.12 < 12.1 < 13
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 1.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)1 is 4 or less, so round down.
- Write the answer. 12.1 ≈ 12 (to the nearest whole number)
Check. Distances: 12.1 − 12 = 0.1 and 13 − 12.1 = 0.9. 12 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 0.7 is between. Rounding to the nearest whole number means choosing the closest whole number.0 < 0.7 < 1
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 7.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)7 is 5 or more, so round up.
- Write the answer. 0.7 ≈ 1 (to the nearest whole number)
Check. Distances: 0.7 − 0 = 0.7 and 1 − 0.7 = 0.3. 1 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 19.5 is between. Rounding to the nearest whole number means choosing the closest whole number.19 < 19.5 < 20
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 5.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)5 is 5 or more, so round up.
- Write the answer. 19.5 ≈ 20 (to the nearest whole number)
Check. Distances: 19.5 − 19 = 0.5 and 20 − 19.5 = 0.5. 20 is the one we choose when exactly halfway. ✓
Watch out. Exactly halfway (like 6.5) always rounds UP.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 2.3 is between. Rounding to the nearest whole number means choosing the closest whole number.2 < 2.3 < 3
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 3.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)3 is 4 or less, so round down.
- Write the answer. 2.3 ≈ 2 (to the nearest whole number)
Check. Distances: 2.3 − 2 = 0.3 and 3 − 2.3 = 0.7. 2 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 6.8 is between. Rounding to the nearest whole number means choosing the closest whole number.6 < 6.8 < 7
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 8.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)8 is 5 or more, so round up.
- Write the answer. 6.8 ≈ 7 (to the nearest whole number)
Check. Distances: 6.8 − 6 = 0.8 and 7 − 6.8 = 0.2. 7 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 9.5 is between. Rounding to the nearest whole number means choosing the closest whole number.9 < 9.5 < 10
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 5.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)5 is 5 or more, so round up.
- Write the answer. 9.5 ≈ 10 (to the nearest whole number)
Check. Distances: 9.5 − 9 = 0.5 and 10 − 9.5 = 0.5. 10 is the one we choose when exactly halfway. ✓
Watch out. Exactly halfway (like 6.5) always rounds UP.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Find the two whole numbers on either side. Then decide which one is closer.
- Find the whole numbers on each side. The whole part of 6.2 is 6, so it is between 6 and 7.6 < 6.2 < 7
- Look at the tenths digit. It tells us if we are past halfway.The tenths digit is 2.
- Choose the closer whole number. 5 or more is closer to the bigger whole number. 4 or less is closer to the smaller one.6.2 is closer to 6.
Check. Distances: 0.2 from 6 and 0.8 from 7. ✓
Watch out. Halfway rounds up.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Find the two whole numbers on either side. Then decide which one is closer.
- Find the whole numbers on each side. The whole part of 14.8 is 14, so it is between 14 and 15.14 < 14.8 < 15
- Look at the tenths digit. It tells us if we are past halfway.The tenths digit is 8.
- Choose the closer whole number. 5 or more is closer to the bigger whole number. 4 or less is closer to the smaller one.14.8 is closer to 15.
Check. Distances: 0.8 from 14 and 0.2 from 15. ✓
Watch out. Halfway rounds up.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Find the two whole numbers on either side. Then decide which one is closer.
- Find the whole numbers on each side. The whole part of 0.4 is 0, so it is between 0 and 1.0 < 0.4 < 1
- Look at the tenths digit. It tells us if we are past halfway.The tenths digit is 4.
- Choose the closer whole number. 5 or more is closer to the bigger whole number. 4 or less is closer to the smaller one.0.4 is closer to 0.
Check. Distances: 0.4 from 0 and 0.6 from 1. ✓
Watch out. Halfway rounds up.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them biggest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths hundredths 2.35 2 . 3 5 2.53 2 . 5 3 2.30 2 . 3 0 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 2.35 has 2, 2.53 has 2, 2.30 has 2. All the same, so look at the next column.
Tenths: 2.35 has 3, 2.53 has 5, 2.30 has 3. Smallest to biggest: 3, 5.
Hundredths: 2.35 has 5, 2.30 has 0. Smallest to biggest: 0, 5. - Write them biggest first. Write the ORIGINAL numbers and check that you have used every one.2.53 m, 2.35 m, 2.30 m
Check. Count them: 3 numbers in the question and 3 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.
Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them smallest first.
- Write the numbers in a place-value table. Line up the decimal points.
ones tenths hundredths 2.35 2 . 3 5 2.53 2 . 5 3 2.30 2 . 3 0 - Compare the columns from the left. Where the digits are the same, look at the next column to the right.Ones: 2.35 has 2, 2.53 has 2, 2.30 has 2. All the same, so look at the next column.
Tenths: 2.35 has 3, 2.53 has 5, 2.30 has 3. Smallest to biggest: 3, 5.
Hundredths: 2.35 has 5, 2.30 has 0. Smallest to biggest: 0, 5. - Write them smallest first. Write the ORIGINAL numbers and check that you have used every one.2.30 m, 2.35 m, 2.53 m
Check. Count them: 3 numbers in the question and 3 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 3.6 is between. Rounding to the nearest whole number means choosing the closest whole number.3 < 3.6 < 4
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 6.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)6 is 5 or more, so round up.
- Write the answer. 3.6 km ≈ 4 km (to the nearest whole number)
Check. Distances: 3.6 − 3 = 0.6 and 4 − 3.6 = 0.4. 4 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 7.2 is between. Rounding to the nearest whole number means choosing the closest whole number.7 < 7.2 < 8
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 2.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)2 is 4 or less, so round down.
- Write the answer. 7.2 litres ≈ 7 litres (to the nearest whole number)
Check. Distances: 7.2 − 7 = 0.2 and 8 − 7.2 = 0.8. 7 is the nearer whole number. ✓
Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.
- Find the two whole numbers that 12.5 is between. Rounding to the nearest whole number means choosing the closest whole number.12 < 12.5 < 13
- Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.The tenths digit is 5.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)5 is 5 or more, so round up.
- Write the answer. 12.5 kg ≈ 13 kg (to the nearest whole number)
Check. Distances: 12.5 − 12 = 0.5 and 13 − 12.5 = 0.5. 13 is the one we choose when exactly halfway. ✓
Watch out. Exactly halfway (like 6.5) always rounds UP.
Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Compare the numbers column by column from the left, not as whole numbers. Give them the same number of decimal places first.
- Look at what Sam did. Sam compared 45 and 5 as if they were whole numbers.45 > 5, so Sam thinks 0.45 > 0.5
- Give both numbers the same number of decimal places. Adding a 0 on the end does not change the value.0.5 = 0.50
- Compare them in a place-value table. Look at the tenths first.
ones tenths hundredths 0.45 0 . 4 5 0.50 0 . 5 0 - Decide who is right. 0.45 < 0.5. Sam is wrong.
Check. On a number line, 0.5 = 0.50 is to the right of 0.45. ✓
Watch out. A decimal with more digits is not always bigger. Compare tenths first, then hundredths.
A 4.5 B 4.4 C 5.4 D 5.5
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. Round each number to the nearest whole number. Look for the ones that round to 5.
- Round each number. Look at the tenths digit. 5 or more rounds up, 4 or less rounds down.A: 4.5 ≈ 5 ✓
B: 4.4 ≈ 4
C: 5.4 ≈ 5 ✓
D: 5.5 ≈ 6 - Choose the two that round to 5. A and C
Check. 4.5 is exactly halfway between 4 and 5 so it rounds up to 5. 5.5 rounds up to 6. ✓
Watch out. Halfway rounds up: 4.5 rounds to 5, and 5.5 rounds to 6.
Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.
Method. A number with one decimal place that rounds to 8 is between 7.5 and 8.4. Find the smallest and the biggest.
- Find the smallest. Numbers below 7.5 round down to 7. 7.5 is halfway, so it rounds up to 8.7.4 rounds to 7 but 7.5 rounds to 8.
- Find the biggest. Numbers from 8.5 up round to 9. 8.4 rounds down to 8.8.4 rounds to 8 but 8.5 rounds to 9, so the biggest is 8.4.
Check. 7.5 ≈ 8 and 8.4 ≈ 8, but 7.4 ≈ 7 and 8.5 ≈ 9. ✓
Watch out. Remember that halfway rounds up.