Watch out
Counting leading zeros as significant figures.
Scottish National 5 Mathematics
National 5 Maths Rounding and significant figures
Round values to a stated number of significant figures and judge suitable accuracy.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Identify place value accurately.
- Know that leading zeros are not significant.
- Use the next digit to decide whether to round up.
Explanation
Decimal places count digits after the decimal point. Significant figures begin at the first non-zero digit and measure the precision of the whole value.
Underline the digit that must remain, inspect the next digit, then round. A next digit of 5 or more increases the retained digit by 1.
In calculations, keep full calculator accuracy during working and round only the final answer to the accuracy requested.
Key formulae and rules
- 0−4: keep the retained digit
- 5−9: increase the retained digit by 1
- significant figures start at the first non-zero digit
Check
Estimate first, then check the sign, order of magnitude and requested accuracy of the final value.
Exam tip
Write the unrounded calculator value, then the rounded answer with the requested accuracy.
Worked examples
Worked example 1
Round to decimal places
Round 18.4762 to 2 decimal places.
- Keep the hundredths digit 7.
- The next digit is 6, so round up.
Answer: 18.48.
Worked example 2
Round to significant figures
Round 0.006384 to 2 significant figures.
- The first significant digit is 6.
- Keep 6 and 3.
- The next digit is 8, so 3 rounds to 4.
So: 0.0064.
Worked example 3
Round a calculation
Calculate 7.8 × 4.63 and give the answer to 3 significant figures.
- Calculator value = 36.114
- Keep 3, 6 and 1.
- The next digit is 1, so do not round up.
Answer: 36.1.
Watch out
- Counting leading zeros as significant figures.
- Rounding intermediate values and losing accuracy.
- Changing the wrong place-value digit.