Year 6 Decimals: Rounding to a degree of accuracy

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.

            14.285
       7 ) 100.000
           0
           -
           10
            7
           --
            30
            28
            --
              20
              14
              --
               60
               56
               --
                40
                35
                --
                 5

2. Start with the first digit, 1. 7 does not go into 1, so this digit of the answer is 0.
   1 ÷ 7 = 0, remainder 1
3. Bring down the next digit, so we have 10. How many 7s go into 10? 1, because 1 × 7 = 7.
   10 ÷ 7 = 1, remainder 3
4. Bring down the next digit, so we have 30. How many 7s go into 30? 4, because 4 × 7 = 28.
   30 ÷ 7 = 4, remainder 2
5. Bring down a 0, so we have 20. Write the decimal point in the answer now, above the point. How many 7s go into 20? 2, because 2 × 7 = 14.
   20 ÷ 7 = 2, remainder 6
6. Bring down a 0, so we have 60. How many 7s go into 60? 8, because 8 × 7 = 56.
   60 ÷ 7 = 8, remainder 4
7. Bring down a 0, so we have 40. How many 7s go into 40? 5, because 5 × 7 = 35.
   40 ÷ 7 = 5, remainder 5
8. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   14.285

Check. Multiply back: 14.285 × 7 is close to 100.

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.
   14.285: the digit in the hundredths column is 8
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.
   14.29

Check. 14.285 lies between 14.28 and 14.29, and 14.29 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. 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.

            5.875
       8 ) 47.000
           0
           -
           47
           40
           --
             70
             64
             --
              60
              56
              --
               40
               40
               --
                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 47. How many 8s go into 47? 5, because 5 × 8 = 40.
   47 ÷ 8 = 5, remainder 7
4. Bring down a 0, so we have 70. Write the decimal point in the answer now, above the point. How many 8s go into 70? 8, because 8 × 8 = 64.
   70 ÷ 8 = 8, remainder 6
5. Bring down a 0, so we have 60. How many 8s go into 60? 7, because 7 × 8 = 56.
   60 ÷ 8 = 7, remainder 4
6. Bring down a 0, so we have 40. How many 8s go into 40? 5, because 5 × 8 = 40.
   40 ÷ 8 = 5, remainder 0
7. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   5.875

Check. 5.875 × 8 = 47. ✓

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. A bus holds 8 children. Round up, because 5 buses would leave some children without a seat.

1. Read the answer. 5.875 means 5 full buses and a bit more.
   5.875 buses
2. Decide the degree of accuracy. We cannot have part of a bus, so round up to the next whole number.
   5.875 buses is not enough, so 6
3. Write the answer. Six buses are needed.
   6 buses

Check. 6 buses hold 6 × 8 = 48 children, which is enough for 47. ✓

Watch out. In a problem about people or things, look at the context. Rounding down can leave someone out.

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.

            4.166
       3 ) 12.500
           0
           -
           12
           12
           --
              5
              3
              -
              20
              18
              --
               20
               18
               --
                2

2. Start with the first digit, 1. 3 does not go into 1, so this digit of the answer is 0.
   1 ÷ 3 = 0, remainder 1
3. Bring down the next digit, so we have 12. How many 3s go into 12? 4, because 4 × 3 = 12.
   12 ÷ 3 = 4, remainder 0
4. Bring down the next digit, so we have 5. Write the decimal point in the answer now, above the point. How many 3s go into 5? 1, because 1 × 3 = 3.
   5 ÷ 3 = 1, remainder 2
5. Bring down the next digit, so we have 20. How many 3s go into 20? 6, because 6 × 3 = 18.
   20 ÷ 3 = 6, remainder 2
6. Bring down a 0, so we have 20. How many 3s go into 20? 6, because 6 × 3 = 18.
   20 ÷ 3 = 6, remainder 2
7. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   4.166

Check. Multiply back: 4.166 × 3 is close to 12.50.

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.
   4.166: 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 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.
   4.17

Check. 4.166 lies between 4.16 and 4.17, and 4.17 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. 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.

           0.42
       7 ) 3.00
           0
           -
            30
            28
            --
             20
             14
             --
              6

2. Start with the first digit, 3. 7 does not go into 3, so this digit of the answer is 0.
   3 ÷ 7 = 0, remainder 3
3. Bring down a 0, so we have 30. Write the decimal point in the answer now, above the point. How many 7s go into 30? 4, because 4 × 7 = 28.
   30 ÷ 7 = 4, remainder 2
4. Bring down a 0, so we have 20. How many 7s go into 20? 2, because 2 × 7 = 14.
   20 ÷ 7 = 2, remainder 6
5. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   0.42

Check. Multiply back: 0.42 × 7 is close to 3.

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 1 decimal place, so look at the tenths column.
   0.42: 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 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.
   0.4

Check. 0.42 lies between 0.4 and 0.5, and 0.4 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. 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.

            33.333
       3 ) 100.000
           0
           -
           10
            9
           --
            10
             9
            --
              10
               9
              --
               10
                9
               --
                10
                 9
                --
                 1

2. Start with the first digit, 1. 3 does not go into 1, so this digit of the answer is 0.
   1 ÷ 3 = 0, remainder 1
3. Bring down the next digit, so we have 10. How many 3s go into 10? 3, because 3 × 3 = 9.
   10 ÷ 3 = 3, remainder 1
4. Bring down the next digit, so we have 10. How many 3s go into 10? 3, because 3 × 3 = 9.
   10 ÷ 3 = 3, remainder 1
5. Bring down a 0, so we have 10. Write the decimal point in the answer now, above the point. How many 3s go into 10? 3, because 3 × 3 = 9.
   10 ÷ 3 = 3, remainder 1
6. Bring down a 0, so we have 10. How many 3s go into 10? 3, because 3 × 3 = 9.
   10 ÷ 3 = 3, remainder 1
7. Bring down a 0, so we have 10. How many 3s go into 10? 3, because 3 × 3 = 9.
   10 ÷ 3 = 3, remainder 1
8. Write the answer. Keep going until the remainder is 0, or until you have the places you need.
   33.333

Check. Multiply back: 33.333 × 3 is close to 100.

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.
   33.333: 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 3
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.
   3 is less than 5, so round down
4. Write the answer. Keep the zeros after the point so the accuracy is clear.
   33.33

Check. 33.333 lies between 33.33 and 33.34, and 33.33 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 smallest number with two decimal places that rounds up to 4.0.

1. Look at the number to be rounded. To round to 4.0, the number must be at least 3.95.
   Rounding to one decimal place: 3.95 → 4.0
2. Check the number below it. 3.94 is less than 3.95, so it rounds to 3.9.
   3.94 → 3.9
3. Write the answer. The smallest number is 3.95.
   3.95

Check. 3.95 rounds up to 4.0, and 3.94 does not. ✓

Watch out. Half-way numbers round up, so 3.95 is the first number that rounds up to 4.0.

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. Write the rounding rule out, then apply it to 6.5.

1. Find the place you are rounding to. The nearest whole number has no decimal places.
   Look at the tenths digit: 5
2. Look at the digit to the right. The digit 5 is 5 or more.
   5 is 5 or more, so round up
3. Decide. Round up to the next whole number.
   6 + 1 = 7

Check. 6.5 is half-way between 6 and 7. Half-way numbers round up. ✓

Watch out. Mo looked at 6 and stopped. He needed the digit after the 6 to decide.

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. Say what the answer means.

1. Write the answer. 6.5 rounds up to 7.
   No, 6.5 rounds up to 7.

Watch out. The answer 6 is what you get when you round down.

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 whole numbers that round to 40 when rounded to the nearest 10.

1. Find the half-way numbers. Numbers from 35 up to 44 are closer to 40 than to 30 or 50. 35 rounds up to 40.
   35 → 40, 44 → 40
2. Check the next numbers. 34 rounds down to 30, and 45 rounds up to 50.
   34 → 30, 45 → 50
3. Count them. Each number from 35 to 44 counts once.
   35, 36, 37, 38, 39, 40, 41, 42, 43, 44
4. Write the answer. There are ten of them.
   10

Check. 10 numbers, from 35 to 44. ✓

Watch out. The range is 5 below and 4 above, because 45 rounds up to 50.