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.
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.
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
- Round 8.764 to 2 decimal places.
- Round 0.006382 to 2 significant figures.
- Round 12,849 to the nearest 1000.
- Estimate 31.2 × 19.7.
- A number is 4.8 to 1 decimal place. Write its lower and upper bounds.
Answers
- 8.76
- 0.0064
- 13,000
- About 600
- Lower bound 4.75, upper bound 4.85
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