Year 6 Arithmetic (SATs): Rounding and estimation
Part of the Year 6 Arithmetic (SATs) place value and the four operations chapter. Chapter overview · whole chapter on one page
Rounding and estimation
Rule
To round to a given place, look at the digit just to the right of that column. If it is 5 or more, round up. If it is 4 or less, round down.
Estimating means rounding each number first, then working with the rounded numbers. It shows whether your answer is about right.
Key ideas
- Round up when the digit to the right is 5, 6, 7, 8 or 9.
- Round down when that digit is 0, 1, 2, 3 or 4.
- Estimate by rounding every number to the same place value.
- An estimate tells you the answer is about right, not the exact answer.
Method. Find the two thousands either side, then look at the hundreds digit.
- Find the two multiples of the rounding amount either side of the number. The number lies between 36,000 and 37,000.36,000 < 36,479 < 37,000
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 4
- Round to the nearest thousand. The digit is 4, which is less than 5, so round down.36,479 rounds to 36,000
- Write the answer. 36,000
Check. 36,000 is 479 less than 36,479, and 37,000 is 521 more. ✓
Watch out. Look at the hundreds digit (4), not the thousands digit.
Method. Look at the digit to the right of the hundred thousands column.
- Find the two multiples of the rounding amount either side of the number. The number lies between 2,800,000 and 2,900,000.2,800,000 < 2,850,000 < 2,900,000
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 5
- Round to the nearest hundred thousand. The digit is 5, which is 5 or more, so round up.2,850,000 rounds to 2,900,000
- Write the answer. 2,900,000
Check. 2,850,000 is halfway between 2,800,000 and 2,900,000, and halves round up. ✓
Method. Round both numbers first, then add the rounded numbers.
- Round the first number. Nearest thousand: 4,912 is nearer to 5,000.4,912 → 5,000
- Round the second number. Nearest thousand: 3,087 is nearer to 3,000.3,087 → 3,000
- Add the rounded numbers. The estimate is about 8,000. The exact answer is 8,000 too.5,000 + 3,000 = 8,000
- Write the answer. 8,000
Check. The exact answer is 7,999, which is close to the estimate of 8,000. ✓
Watch out. An estimate can be close but not exact: 7,999 and 8,000 differ by 1.
Exercise 1C Practice: rounding and estimating
Non-calculatorMethod. Look at the tens digit.
- Find the two multiples of the rounding amount either side of the number. The number lies between 8,400 and 8,500.8,400 < 8,463 < 8,500
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 6
- Round to the nearest hundred. The digit is 6, which is 5 or more, so round up.8,463 rounds to 8,500
- Write the answer. 8,500
Check. 8,500 is 37 more than 8,463, and 8,400 is 63 less. ✓
Method. Look at the hundreds digit.
- Find the two multiples of the rounding amount either side of the number. The number lies between 58,000 and 59,000.58,000 < 58,241 < 59,000
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 2
- Round to the nearest thousand. The digit is 2, which is less than 5, so round down.58,241 rounds to 58,000
- Write the answer. 58,000
Check. 58,000 is the nearest thousand. ✓
Method. Look at the ones digit.
- Find the two multiples of the rounding amount either side of the number. The number lies between 670 and 680.670 < 672 < 680
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 2
- Round to the nearest ten. The digit is 2, which is less than 5, so round down.672 rounds to 670
- Write the answer. 670
Check. 670 is nearer to 672 than 680 is. ✓
Method. Look at the ten thousands digit.
- Find the two multiples of the rounding amount either side of the number. The number lies between 3,400,000 and 3,500,000.3,400,000 < 3,465,000 < 3,500,000
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 6
- Round to the nearest hundred thousand. The digit is 6, which is 5 or more, so round up.3,465,000 rounds to 3,500,000
- Write the answer. 3,500,000
Check. 3,500,000 is nearer than 3,400,000. ✓
Method. Look at the hundred thousands digit.
- Find the two multiples of the rounding amount either side of the number. The number lies between 9,000,000 and 10,000,000.9,000,000 < 9,999,997 < 10,000,000
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 9
- Round to the nearest million. The digit is 9, which is 5 or more, so round up.9,999,997 rounds to 10,000,000
- Write the answer. 10,000,000
Check. 10,000,000 is 3 more than 9,999,997. ✓
Watch out. Rounding can change the number of digits: 9 million rounds up to 10 million.
Method. Look at the thousands digit.
- Find the two multiples of the rounding amount either side of the number. The number lies between 410,000 and 420,000.410,000 < 412,000 < 420,000
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 2
- Round to the nearest ten thousand. The digit is 2, which is less than 5, so round down.412,000 rounds to 410,000
- Write the answer. 410,000
Check. 410,000 is 2,000 less, and 420,000 is 8,000 more. ✓
Method. Look at the hundreds digit.
- Find the two multiples of the rounding amount either side of the number. The number lies between 15,000 and 16,000.15,000 < 15,608 < 16,000
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 6
- Round to the nearest thousand. The digit is 6, which is 5 or more, so round up.15,608 rounds to 16,000
- Write the answer. 16,000
Check. 16,000 is 392 more than 15,608. ✓
Method. Round each number, then subtract.
- Round 48,207. Nearest 10,000 is 50,000.48,207 → 50,000
- Round 19,586. Nearest 10,000 is 20,000.19,586 → 20,000
- Subtract. The estimate is 30,000.50,000 - 20,000 = 30,000
- Write the answer. 30,000
Check. The exact answer is 28,621, which is close to 30,000. ✓
Method. Round to the nearest 100.
- Find the two multiples of the rounding amount either side of the number. The number lies between 2,400 and 2,500.2,400 < 2,465 < 2,500
- Look at the digit just to the right of the rounding column. It shows which multiple is nearer.digit 6
- Round to the nearest hundred. The digit is 6, which is 5 or more, so round up.2,465 rounds to 2,500
- Write the answer. 2,500
Check. 2,500 is nearer to 2,465 than 2,400 is. ✓
Watch out. A rounding to 2,400 would be wrong here because 65 is more than 50.
Method. Estimate the answer, then compare it with Sam's answer.
- Round the numbers. 3,812 → 4,000 and 5,190 → 5,000.4,000 + 5,000
- Estimate. The answer should be about 9,000.4,000 + 5,000 = 9,000
- Compare with Sam's answer. 8,002 is about 1,000 less than 9,000, so it is not sensible.8,002 is not about 9,000
- Write the answer. No
Check. The exact answer is 9,002, so Sam is wrong: 8,002 is about 1,000 too small. ✓
Method. Round in two steps, then round the original number once and compare.
- Round to the nearest 100. The tens digit is 5, so 1,450 rounds up to 1,500.1,450 → 1,500
- Round that to the nearest 1,000. The hundreds digit is 5, so 1,500 rounds up to 2,000.1,500 → 2,000
- Round 1,450 once to the nearest 1,000. The hundreds digit is 4, so it rounds down to 1,000.1,450 → 1,000
- Write the answer. 2,000 (two steps) and 1,000 (one step); not the same
Check. The two methods give different answers, so the rounding must not be done in steps. ✓
Watch out. Round the original number once when you can. Rounding in steps can change the answer.
Method. Look at which digit is next to each column.
- Round to the nearest 1,000. The hundreds digit is 4, so round down.8,000
- Round to the nearest 100. The tens digit is 5, so round up.8,500
- Write the answer. Because the hundreds digit is 4, so it rounds down to 8,000 at the thousand level, but the tens digit is 5, so it rounds up to 8,500 at the hundred level.
Check. Different columns use different digits. ✓