Rounding and Estimation

Rounding and estimation are important GCSE Maths skills. They help you give answers to a suitable level of accuracy and check whether your calculations are sensible.

Common rounding instructions include:

nearest 10, 100 or 1000

1, 2 or 3 decimal places

1, 2 or 3 significant figures

Rounding to decimal places

Decimal places count the number of digits after the decimal point.

Example 1: Round to 2 decimal places

Round 7.386 to 2 decimal places.

The second decimal place is 8. The next digit is 6.

Since 6 is 5 or more, round up.

7.386 ≈ 7.39

Rounding to significant figures

Significant figures start from the first non-zero digit.

Example 2: Round to 3 significant figures

Round 0.004728 to 3 significant figures.

The first significant digit is 4.

The first three significant digits are 4, 7 and 2.

The next digit is 8, so round up.

0.004728 ≈ 0.00473

Rounding to the nearest 10, 100 or 1000

Example 3: Round to the nearest 100

Round 3,748 to the nearest 100.

The hundreds digit is 7. The next digit is 4.

Since 4 is less than 5, keep the 7 the same.

3,748 ≈ 3,700

Estimation

Estimation means rounding numbers first to make a calculation easier. It is often used to check whether an answer is reasonable.

Example 4: Estimate a calculation

Estimate 49.8 × 19.6.

Round each number to 1 significant figure:

49.8 ≈ 50

19.6 ≈ 20

Now multiply:

50 × 20 = 1000

Using estimation to check answers

Estimation is useful because it helps you spot decimal place errors.

Example 5: Check if an answer is sensible

A calculator gives:

38.9 × 21.2 = 824.68

Estimate:

40 × 20 = 800

Since 824.68 is close to 800, the calculator answer is sensible.

Bounds

Bounds show the smallest and largest possible values that could round to a given number.

Example 6: Bounds for a rounded number

A length is 6.4 cm to 1 decimal place.

The lower bound is halfway between 6.3 and 6.4:

6.35

The upper bound is halfway between 6.4 and 6.5:

6.45

So the actual length is at least 6.35 cm but less than 6.45 cm.

Common mistake:

A common mistake is confusing decimal places with significant figures. For example, 0.0456 to 2 decimal places is 0.05, but to 2 significant figures it is 0.046.

Exam tip:

In estimation questions, round numbers to simple values that make the calculation easy. In checking questions, your estimate does not need to be exact; it needs to show the answer is reasonable.

Video explanation

A short Worthing Maths Tutor video explanation for rounding and estimation can be embedded here later to improve student engagement and time on page.

Practice questions

  1. Round 8.764 to 2 decimal places.
  2. Round 0.006382 to 2 significant figures.
  3. Round 12,849 to the nearest 1000.
  4. Estimate 31.2 × 19.7.
  5. A number is 4.8 to 1 decimal place. Write its lower and upper bounds.

Answers

  1. 8.76
  2. 0.0064
  3. 13,000
  4. About 600
  5. Lower bound 4.75, upper bound 4.85

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