These questions ask you to choose or produce a sensible estimate for a decimal calculation and sometimes to compare that estimate with the exact value. A good estimate uses nearby numbers that make the original operation easy.
Choose benchmarks, keep the operation, check the scale
First identify whether the calculation adds, subtracts, multiplies, or divides. Replace each operand with a nearby number that works smoothly with that operation. Then calculate with the benchmarks and compare the size with the original values. For multiplication, 17.8 × 3.1 is close to 18 × 3 = 54. For division, 62.4 ÷ 7.8 is close to 64 ÷ 8 = 8. For addition, 4.42 + 2.61 is close to 4 + 3 = 7. For subtraction, 21.2 - 6.1 is close to 21 - 6 = 15. None of these steps changes the operation.
| Calculation | Useful benchmark feature |
|---|---|
| Addition or subtraction | Choose nearby values with matching place value that are easy to combine. |
| Multiplication | Choose nearby factors with a familiar product, while preserving the effect of any factor below 1. |
| Division | Choose compatible values whose quotient is easy, and keep the expected number of groups in view. |
| A required benchmark is stated | Use the stated values exactly; do not replace them with a different rounding plan. |
Direction gives another self-check for sums. If both addends round up, their rounded sum is above the exact sum; if both round down, it is below. For example, 3.6 + 1.7 rounds up to 4 + 2 = 6, so the exact sum must be lower than 6. Mixed directions alone do not settle the comparison.
Common wrong turns
| Tempting route | How to reject it |
|---|---|
| Round correctly but switch multiplication to addition | Benchmarks simplify the numbers, not the relationship between them. Copy the operation sign before calculating. |
| Switch addition to subtraction or division to addition | Say the original operation in words, then apply that same action to the benchmarks. |
| Lose a power of ten | Compare orders of magnitude. A product involving tens and whole units should not suddenly look like tenths or thousands without a reason. |
| Ignore a factor or divisor below 1 | Multiplication by a proper decimal shrinks the other factor, while division by a proper decimal enlarges the dividend. Preserve that size relationship. |
| Claim equality after rounding | Rounding usually discards part of the value. Track whether each operand moved up or down before comparing the estimate with the exact result. |
Try it
Which is the best estimate for 48.8 ÷ 9.9?
- 0.5
- 5
- 50
- 500
A rectangular garden is 24.8 metres long and 3.1 metres wide. Estimate by using 25 metres and 3 metres. Enter the estimated area in square metres.
A scientist combines readings of 0.198 and 0.304. Which is the best estimate of their sum?
- 0.05
- 0.2
- 0.5
- 5