Year 6 Decimals: check-up and SATs-style questions

Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).

Method. Find the column of the digit, then multiply the digit by the value of that column.

1. Find the column of the digit. Count the places from the decimal point.
   The 7 is in the hundredths column
2. Find what one of that column is worth. Each hundredth is worth 0.01.
   1 hundredth = 0.01
3. Multiply the digit by that value. The digit tells us how many of them there are.
   7 × 0.01 = 0.07
4. Write the answer. Keep the zeros that show the place.
   0.07

Check. 5.472 = 5 + 0.4 + 0.07 + 0.002. ✓

Watch out. The 0 digits still count as places. The digit 7 is worth 0.07, not 7.

Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).

Method. Count the hundredths: there are 100 of them in each whole, so multiply by 100.

1. Write 4.07 with 2 decimal places. Zeros at the end do not change the value, but they show the place.
   4.07
2. Find how many hundredths make one whole. Each whole one has 100 hundredths.
   1 × 100 = 100
3. Count the hundredths in 4.07. Multiply by 100, because each whole has 100 of them.
   4.07 × 100 = 407
4. Write the answer. The answer is a count, so it is a whole number.
   407

Check. 407 hundredths are 407 × 0.01 = 4.07. ✓

Watch out. Each hundredth is 0.01, so a count of 407 is worth 4.07.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 2 places to the left. The decimal point does not move.

1. Count how many places the digits move. 100 is 2 zeros, so each digit moves 2 places to the left.
   6.4 × 100
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   6.4 moves 2 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   640

Check. Undo it: 640 ÷ 100 gives 6.4 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 1 place to the right. The decimal point does not move.

1. Count how many places the digits move. 10 is 1 zero, so each digit moves 1 place to the right.
   0.09 ÷ 10
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.09 moves 1 place to the right
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   0.009

Check. Undo it: 0.009 × 10 gives 0.09 again. ✓

Watch out. Dividing makes the number smaller, so the digits move to the right. Keep a zero in the ones place when the answer is less than 1.

Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.

Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.

1. Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.

    4.36
     × 7
   -----
   30.52

2. Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.
   6 × 7 = 42, write 2 and carry 4
   3 × 7 = 21 + 4 carried = 25, write 5 and carry 2
   4 × 7 = 28 + 2 carried = 30, write 0 and carry 3
   write 3
3. Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.
   436 × 7 = 3052, and 3052 → 30.52

Check. About 4 × 7 = 28, and 30.52 is close to that. ✓

Watch out. Count the decimal places in the question. Do not count the zeros you carry.

Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.

Method. Multiply as if there were no decimal point. Then put the point back so the answer has 1 decimal place.

1. Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.

    5.4
    × 8
   ----
   43.2

2. Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.
   4 × 8 = 32, write 2 and carry 3
   5 × 8 = 40 + 3 carried = 43, write 3 and carry 4
   write 4
3. Count the decimal places and put the point back. The decimal number has 1 decimal place, so the answer has 1 decimal place.
   54 × 8 = 432, and 432 → 43.2

Check. About 5 × 8 = 40, and 43.2 is close to that. ✓

Watch out. Count the decimal places in the question. Do not count the zeros you carry.

Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, and the remainder is what is left over. Bring down a 0 after the decimal point to keep going.

Method. Share the number out one digit at a time. Put the decimal point in the answer when you reach it in the number.

1. Set out the layout. The number being divided goes inside the bracket. The answer goes above it.

           0.9
       4 ) 3.6
           0
           -
            36
            36
            --
             0

2. Start with the first digit, 3. 4 does not go into 3, so this digit of the answer is 0.
   3 ÷ 4 = 0, remainder 3
3. Bring down the next digit, so we have 36. Write the decimal point in the answer now, above the point. How many 4s go into 36? 9, because 9 × 4 = 36.
   36 ÷ 4 = 9, remainder 0
4. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   0.9

Check. 0.9 × 4 = 3.6. ✓

Watch out. Do not forget the decimal point in the answer. Bring down zeros only after you have used all the digits of the number.

Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, and the remainder is what is left over. Bring down a 0 after the decimal point to keep going.

Method. Share the number out one digit at a time. Put the decimal point in the answer when you reach it in the number.

1. Set out the layout. The number being divided goes inside the bracket. The answer goes above it.

            2.3
       5 ) 11.5
           0
           -
           11
           10
           --
             15
             15
             --
              0

2. Start with the first digit, 1. 5 does not go into 1, so this digit of the answer is 0.
   1 ÷ 5 = 0, remainder 1
3. Bring down the next digit, so we have 11. How many 5s go into 11? 2, because 2 × 5 = 10.
   11 ÷ 5 = 2, remainder 1
4. Bring down the next digit, so we have 15. Write the decimal point in the answer now, above the point. How many 5s go into 15? 3, because 3 × 5 = 15.
   15 ÷ 5 = 3, remainder 0
5. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   2.3

Check. 2.3 × 5 = 11.5. ✓

Watch out. Do not forget the decimal point in the answer. Bring down zeros only after you have used all the digits of the number.

Key words. To round to a degree of accuracy, find the place you are rounding to and look at the digit to its right. 5 or more means round up. Less than 5 means round down.

Method. Find the place, look at the digit to its right, then round up or stay the same.

1. Find the place you are rounding to. We want 2 decimal places, so look at the hundredths column.
   6.4375: the digit in the hundredths column is 3
2. Look at the digit to its right. This digit decides whether the number goes up or stays the same.
   The digit to the right is 7
3. Decide whether to round up or down. If the digit is 5 or more, round up. If it is less than 5, keep the same digit.
   7 is 5 or more, so round up
4. Write the answer. Keep the zeros after the point so the accuracy is clear.
   6.44

Check. 6.4375 lies between 6.43 and 6.44, and 6.44 is the nearer one. ✓

Watch out. Look only at the digit to the right of the place you are rounding to. Do not round the digits one at a time.

Key words. To round to a degree of accuracy, find the place you are rounding to and look at the digit to its right. 5 or more means round up. Less than 5 means round down.

Method. Find the place, look at the digit to its right, then round up or stay the same.

1. Find the place you are rounding to. We want 1 decimal place, so look at the tenths column.
   27.46: the digit in the tenths column is 4
2. Look at the digit to its right. This digit decides whether the number goes up or stays the same.
   The digit to the right is 6
3. Decide whether to round up or down. If the digit is 5 or more, round up. If it is less than 5, keep the same digit.
   6 is 5 or more, so round up
4. Write the answer. Keep the zeros after the point so the accuracy is clear.
   27.5

Check. 27.46 lies between 27.4 and 27.5, and 27.5 is the nearer one. ✓

Watch out. Look only at the digit to the right of the place you are rounding to. Do not round the digits one at a time.

Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).

Method. Find the column of the digit, then multiply the digit by the value of that column.

1. Find the column of the digit. Count the places from the decimal point.
   The 6 is in the thousandths column
2. Find what one of that column is worth. Each thousandth is worth 0.001.
   1 thousandth = 0.001
3. Multiply the digit by that value. The digit tells us how many of them there are.
   6 × 0.001 = 0.006
4. Write the answer. Keep the zeros that show the place.
   0.006

Check. 3.206 = 3 + 0.2 + 0.006. ✓

Watch out. The 0 digits still count as places. The digit 6 is worth 0.006, not 6.

Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.

Method. Each digit moves 3 places to the left. The decimal point does not move.

1. Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the left.
   0.37 × 1000
2. Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.
   0.37 moves 3 places to the left
3. Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.
   370

Check. Undo it: 370 ÷ 1000 gives 0.37 again. ✓

Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.

Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.

Method. Multiply as if there were no decimal point. Then put the point back so the answer has 1 decimal place.

1. Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.

    8.6
    × 7
   ----
   60.2

2. Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.
   6 × 7 = 42, write 2 and carry 4
   8 × 7 = 56 + 4 carried = 60, write 0 and carry 6
   write 6
3. Count the decimal places and put the point back. The decimal number has 1 decimal place, so the answer has 1 decimal place.
   86 × 7 = 602, and 602 → 60.2

Check. About 9 × 7 = 63, and 60.2 is close to that. ✓

Watch out. Count the decimal places in the question. Do not count the zeros you carry.

Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.

Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.

1. Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.

    2.76
     × 5
   -----
   13.80

2. Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.
   6 × 5 = 30, write 0 and carry 3
   7 × 5 = 35 + 3 carried = 38, write 8 and carry 3
   2 × 5 = 10 + 3 carried = 13, write 3 and carry 1
   write 1
3. Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.
   276 × 5 = 1380, and 1380 → 13.80

Check. About 3 × 5 = 15, and 13.80 is close to that. ✓

Watch out. Count the decimal places in the question. Do not count the zeros you carry.

Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, and the remainder is what is left over. Bring down a 0 after the decimal point to keep going.

Method. Share the number out one digit at a time. Put the decimal point in the answer when you reach it in the number.

1. Set out the layout. The number being divided goes inside the bracket. The answer goes above it.

           2.3
       4 ) 9.2
           8
           -
            12
            12
            --
             0

2. Start with the first digit, 9. How many 4s go into 9? 2, because 2 × 4 = 8.
   9 ÷ 4 = 2, remainder 1
3. Bring down the next digit, so we have 12. Write the decimal point in the answer now, above the point. How many 4s go into 12? 3, because 3 × 4 = 12.
   12 ÷ 4 = 3, remainder 0
4. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   2.3

Check. 2.3 × 4 = 9.2. ✓

Watch out. Do not forget the decimal point in the answer. Bring down zeros only after you have used all the digits of the number.

Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, and the remainder is what is left over. Bring down a 0 after the decimal point to keep going.

Method. Share the number out one digit at a time. Put the decimal point in the answer when you reach it in the number.

1. Set out the layout. The number being divided goes inside the bracket. The answer goes above it.

            5.7
       8 ) 45.6
           0
           -
           45
           40
           --
             56
             56
             --
              0

2. Start with the first digit, 4. 8 does not go into 4, so this digit of the answer is 0.
   4 ÷ 8 = 0, remainder 4
3. Bring down the next digit, so we have 45. How many 8s go into 45? 5, because 5 × 8 = 40.
   45 ÷ 8 = 5, remainder 5
4. Bring down the next digit, so we have 56. Write the decimal point in the answer now, above the point. How many 8s go into 56? 7, because 7 × 8 = 56.
   56 ÷ 8 = 7, remainder 0
5. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   5.7

Check. 5.7 × 8 = 45.6. ✓

Watch out. Do not forget the decimal point in the answer. Bring down zeros only after you have used all the digits of the number.

Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).

Method. Write the numbers with the same number of places, then compare them from the left.

1. Write both numbers with the same number of decimal places. Add zeros at the end so the places line up.
   0.704 and 0.740
2. Compare the whole numbers, then the tenths, then the hundredths. Start at the left. The first place where the digits differ decides.
   0704 and 0740 (without the point)
3. Choose the symbol. The bigger number is on the open side of the symbol.
   0.704 < 0.740

Check. Compare the two numbers on a number line: the one further right is bigger. ✓

Watch out. 0.5 is bigger than 0.45, even though 45 is less than 5 when you read the digits alone.

Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, and the remainder is what is left over. Bring down a 0 after the decimal point to keep going.

Method. Share the number out one digit at a time. Put the decimal point in the answer when you reach it in the number.

1. Set out the layout. The number being divided goes inside the bracket. The answer goes above it.

           1.875
       4 ) 7.500
           4
           -
            35
            32
            --
             30
             28
             --
              20
              20
              --
               0

2. Start with the first digit, 7. How many 4s go into 7? 1, because 1 × 4 = 4.
   7 ÷ 4 = 1, remainder 3
3. Bring down the next digit, so we have 35. Write the decimal point in the answer now, above the point. How many 4s go into 35? 8, because 8 × 4 = 32.
   35 ÷ 4 = 8, remainder 3
4. Bring down the next digit, so we have 30. How many 4s go into 30? 7, because 7 × 4 = 28.
   30 ÷ 4 = 7, remainder 2
5. Bring down a 0, so we have 20. How many 4s go into 20? 5, because 5 × 4 = 20.
   20 ÷ 4 = 5, remainder 0
6. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   1.875

Check. Multiply back: 1.875 × 4 is close to 7.50.

Watch out. Do not forget the decimal point in the answer. Bring down zeros only after you have used all the digits of the number.

Key words. To round to a degree of accuracy, find the place you are rounding to and look at the digit to its right. 5 or more means round up. Less than 5 means round down.

Method. Find the place, look at the digit to its right, then round up or stay the same.

1. Find the place you are rounding to. We want 2 decimal places, so look at the hundredths column.
   1.875: the digit in the hundredths column is 7
2. Look at the digit to its right. This digit decides whether the number goes up or stays the same.
   The digit to the right is 5
3. Decide whether to round up or down. If the digit is 5 or more, round up. If it is less than 5, keep the same digit.
   5 is 5 or more, so round up
4. Write the answer. Keep the zeros after the point so the accuracy is clear.
   1.88

Check. 1.875 lies between 1.87 and 1.88, and 1.88 is the nearer one. ✓

Watch out. Look only at the digit to the right of the place you are rounding to. Do not round the digits one at a time.

Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.

Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.

1. Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.

   1.85
    × 4
   ----
   7.40

2. Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.
   5 × 4 = 20, write 0 and carry 2
   8 × 4 = 32 + 2 carried = 34, write 4 and carry 3
   1 × 4 = 4 + 3 carried = 7, write 7
3. Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.
   185 × 4 = 740, and 740 → 7.40

Check. About 2 × 4 = 8, and 7.40 is close to that. ✓

Watch out. Count the decimal places in the question. Do not count the zeros you carry.

Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.

Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.

1. Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.

   0.65
    × 2
   ----
   1.30

2. Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.
   5 × 2 = 10, write 0 and carry 1
   6 × 2 = 12 + 1 carried = 13, write 3 and carry 1
   write 1
3. Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.
   65 × 2 = 130, and 130 → 1.30

Check. About 1 × 2 = 2, and 1.30 is close to that. ✓

Watch out. Count the decimal places in the question. Do not count the zeros you carry.

Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).

Method. Line up the decimal points, then add each column from the right.

1. Write the numbers under each other. Line up the decimal points in one column. Fill the gaps with zeros.

     7.40
   + 1.30
   ------
     8.70

2. Add column by column, from the right. Carry any ten into the next column to the left.
   7.40 + 1.30 = 8.70
3. Write the answer with its decimal point in the same column. The decimal points line up in the question and in the answer.
   8.70

Check. Add the numbers in a different order and you get 8.70 again. ✓

Watch out. Line up the decimal points, not the last digits. Fill the gaps with zeros.

Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.

Method. Take the total from £20.00.

1. Write £20 with two decimal places. This lines up the subtraction.
   20.00 − 8.70
2. Subtract. Borrow when you need to.
   20.00 − 8.70 = 11.30
3. Write the answer. This is the change.
   11.30

Check. 8.70 + 11.30 = 20.00. ✓

Watch out. Find the total of everything first, then take it from the money paid.

Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, and the remainder is what is left over. Bring down a 0 after the decimal point to keep going.

Method. Share the number out one digit at a time. Put the decimal point in the answer when you reach it in the number.

1. Set out the layout. The number being divided goes inside the bracket. The answer goes above it.

            1.562
       8 ) 12.500
           0
           -
           12
            8
           --
             45
             40
             --
              50
              48
              --
               20
               16
               --
                4

2. Start with the first digit, 1. 8 does not go into 1, so this digit of the answer is 0.
   1 ÷ 8 = 0, remainder 1
3. Bring down the next digit, so we have 12. How many 8s go into 12? 1, because 1 × 8 = 8.
   12 ÷ 8 = 1, remainder 4
4. Bring down the next digit, so we have 45. Write the decimal point in the answer now, above the point. How many 8s go into 45? 5, because 5 × 8 = 40.
   45 ÷ 8 = 5, remainder 5
5. Bring down a 0, so we have 50. How many 8s go into 50? 6, because 6 × 8 = 48.
   50 ÷ 8 = 6, remainder 2
6. Bring down a 0, so we have 20. How many 8s go into 20? 2, because 2 × 8 = 16.
   20 ÷ 8 = 2, remainder 4
7. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   1.562

Check. Multiply back: 1.562 × 8 is close to 12.5.

Watch out. Do not forget the decimal point in the answer. Bring down zeros only after you have used all the digits of the number.

Key words. To round to a degree of accuracy, find the place you are rounding to and look at the digit to its right. 5 or more means round up. Less than 5 means round down.

Method. Find the place, look at the digit to its right, then round up or stay the same.

1. Find the place you are rounding to. We want 2 decimal places, so look at the hundredths column.
   1.562: the digit in the hundredths column is 6
2. Look at the digit to its right. This digit decides whether the number goes up or stays the same.
   The digit to the right is 2
3. Decide whether to round up or down. If the digit is 5 or more, round up. If it is less than 5, keep the same digit.
   2 is less than 5, so round down
4. Write the answer. Keep the zeros after the point so the accuracy is clear.
   1.56

Check. 1.562 lies between 1.56 and 1.57, and 1.56 is the nearer one. ✓

Watch out. Look only at the digit to the right of the place you are rounding to. Do not round the digits one at a time.