Lesson 14.1 · 20 min

Estimating Calculations

Rounding every number to one significant figure to get a quick estimate — and using it to catch wrong answers.

In this lesson you will learn to…

Round numbers to one significant figure
Estimate the answer to a calculation, including negatives and divisions
Use an estimate to pick the correct answer from a list
Use an estimate to show that an answer is definitely wrong

Why this matters

Calculators are only as good as the buttons you press. A quick estimate — done in your head in a few seconds — is the best protection against a misplaced decimal point, whether you are checking a shopping bill, a medicine dose or an exam answer.

Dividing by small numbers

Estimating $6.72 \div 320$ : $7 \div 300 \approx 0.02$ . Dividing by a large number gives a small answer. Estimating $14.08 \div 32.2$ : $14 \div 30 \approx 0.5$ .

Estimates are not exact. Two different sensible estimates can both be fine. The point is to be close enough to catch a big mistake, not to get the exact answer.

Key rules and formulas

Round to 1 significant figure
$11.7 \to 10$ , $2.8 \to 3$ , $0.96 \to 1$ , $32.2 \to 30$ , $0.068 \to 0.07$ . Keep only the first non-zero digit.
Make it easy
Sometimes choose friendlier numbers: $13.8 \div 6.8 \approx 14 \div 7 = 2$ is easier than $10 \div 7$ .
Use the symbol ≈
$11.7 \div 2.8 \approx 12 \div 3 = 4$
" $\approx$ " means "is approximately equal to".
Checking
If a calculator answer is far from your estimate, you have probably pressed a wrong key or put the decimal point in the wrong place.

Worked examples

Worked example 1

A single calculation

Estimate

4.1 \times 0.9

and

- 6.32 \div 1.87

Try it yourself first, then reveal the solution one step at a time.

Worked example 2

A fraction

Estimate

\frac{39 \times 71}{54}

Try it yourself first, then reveal the solution one step at a time.

Worked example 3

Spotting a wrong answer

24.318 \div 19.3 = 21.6

correct?

Try it yourself first, then reveal the solution one step at a time.

Practice: estimating

8 questions

Eight questions. Estimates within a sensible range are accepted.

Question 1 of 8Quick-fire drill
Quick-fire: round to 1 significant figure.
10 questions · 60 seconds · answer as many as you can.
Question 2 of 8Type the answerFoundation
Estimate $11.7 \div 2.8$ .
Your answer
Question 3 of 8Type the answer
Estimate $8.24 \div - 0.96$ .
Your answer
Question 4 of 8Match the pairs
Use estimation to match each calculation with its answer (to 2 d.p.).
Pick an answer, then choose the row it belongs to. You can also drag it.
- $\frac{39 \times 71}{54}$
- $\frac{28 \times 18}{589}$
- $\frac{31 \times 7.9}{3021}$
- $\frac{501 \times 81.2}{30.9}$
Question 5 of 8Choose all that apply
Using estimation, select every calculation that is definitely incorrect.
Select every correct answer — there may be more than one.
$21.2 \times 0.43 = 9.116$ $\frac{4.98 + 3.67}{1.8} = 1.015$ $0.455 \times 18.4 = 8.372$ $24.318 \div 19.3 = 21.6$
Question 6 of 8Type the answer
Estimate $14.08 \div 32.2$ .
Your answer
Question 7 of 8Type the answer
Estimate $- 123.69 \div 1.9$ .
Your answer
Question 8 of 8True or false
$6.72 \div 320$ is approximately 2.

In this lesson you will learn to…

Why this matters

Dividing by small numbers

Key rules and formulas

Round to 1 significant figure

Make it easy

Use the symbol ≈

Checking

Worked examples

Practice: estimating