Year 8 · Maths

Estimate Calculations by Rounding

4 checked activities 2 video matches

How do you estimate an answer by rounding?

Round each number to one significant figure, carry out the simpler calculation, and write the result as an estimate using the symbol ≈. For example, 312 × 48 ≈ 300 × 50 = 15,000. Compare the estimate with the exact answer to check whether the exact answer is sensible.

Two worked estimates

Multiplication: 312 × 48 ≈ 300 × 50 = 15,000.
Division: 19.6 ÷ 3.9 ≈ 20 ÷ 4 = 5.

Examples: 4.87 + 19.2 ≈ 5 + 20 = 25 · 0.0473 to 1 significant figure is 0.05

Keep practising: Use the Year 8 Maths checklist

Try the estimate-then-check routine

Round both numbers to one significant figure, calculate the estimate, then compare its scale with the exact result.

Worked example: 49.7 x 19.8 is about 50 x 20 = 1,000. The exact answer is 984.06, so the estimate confirms the scale.

Understand the key idea

Estimating means rounding each number — usually to one significant figure — then doing the easier calculation in your head. The result is not the exact answer; it tells you roughly what the answer should be, so you can spot a calculation that has gone badly wrong. The symbol ≈ means "is approximately equal to".

Five further estimation questions with complete working

3.97 × 19.8 ≈ 4 × 20 = 80.
58.7 × 0.21 ≈ 60 × 0.2 = 12.
803 ÷ 19.8 ≈ 800 ÷ 20 = 40.
0.48 × 198 ≈ 0.5 × 200 = 100.
49.8 × 2.03 = 1010.94 is not sensible because the estimate is about 50 × 2 = 100. The correct exact product is 101.094.

Common mix-up

Rounding to one significant figure is not the same as rounding to one decimal place. To 1 s.f. 0.0473 is 0.05, while to 1 d.p. it is 0.0.

Try this first

Estimate 312 × 48 by rounding each number to 1 significant figure.
Decide whether 19.6 ÷ 3.9 ≈ 5 is a sensible check.
Round 0.0473 to 1 significant figure and to 1 decimal place, and compare.

Ask: Your calculator says 2,000 — how could you tell quickly whether that is sensible?

Year 8 learners practise estimating answers by rounding.

The activities include Estimate By Rounding to One Significant Figure Using Decimal Numbers, Estimate Measures, Estimate with Decimals, and related practice. The checked support below includes worksheet, teaching, lesson, video. Open a resource in its provider's website and choose the format that best helps the learner explain the idea independently.

Activities covered

Estimate By Rounding to One Significant Figure Using Decimal Numbers
Estimate Measures
Estimate with Decimals
Estimate with Whole Numbers

Learning path

These same-subject links were reviewed as the foundations for this topic and the learning it directly unlocks.

Learn this first

Year 6Use Estimation To Check Answers
Introduces estimation as a reasonableness check before significant-figure estimates are formalised.
Year 8Round Approximate Numbers Appropriately
Accurate rounding to an appropriate place is the operation used to create an estimate.

Where this leads next

Year 8Use Calculators Technology For Accuracy
Pairs an estimate with an accurate calculator result so implausible entries or operations can be detected.
Year 9Round Approximate Numbers Appropriately
Carries estimation into later multistep work where the required degree of accuracy must be chosen.

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