National 5 Maths
Rounding
Course content
- Rounding to a given number of significant figures or decimal places.
Rules for significant figures
- All non-zero digits are significant.
- Zeros between non-zero digits are significant, because without them the value of the number would change, eg. 208, 30082.
- Zeros at the start of decimal numbers are not significant, because they are only used to position a decimal point, eg. 0.02, 0.000805.
- Zeros at the end are significant only if they are to the right of the decimal point, because they show accuracy, eg. 125.50 but not 2040.
Textbook page references
- TeeJay Maths N4 Book 2 page 28
- Zeta National 5+ Maths pp.1-4
- Leckie National 5 Maths pp.84-88
Self-study course
- National5.com
Highly recommended. Save £10 with discount code 'Maths.scot'.
Examples
- 208 has 3 significant figures
- 30082 has 5 significant figures
- 0.02 has 1 significant figure
- 0.000805 has 3 significant figures
- 125.50 has 5 significant figures
- 2040 has 3 significant figures
- 98.2 has 3 significant figures
- 450 has 2 significant figures
- 1.00023 has 6 significant figures
- 0.999 has 3 significant figures
- 9.99 has 3 significant figures
Rounding examples
- 208 rounded to 2 sig. fig. is 210
- 30082 rounded to 3 sig. fig. is 30100
- 0.02 rounded to 1 sig. fig. is 0.02
- 0.000805 rounded to 2 sig. fig. is 0.00081
- 125.50 rounded to 2 sig. fig. is 130
- 2040 rounded to 2 sig. fig. is 2000
- 98.2 rounded to 1 sig. fig. is 100
- 450 rounded to 1 sig. fig. is 500
- 1.00023 rounded to 3 sig. fig. is 1.00
- 0.999 rounded to 2 sig. fig. is 1.0
- 9.99 rounded to 2 sig. fig. is 10. This may seem strange, because the number 10 only has 1 significant figure, but 9.99 rounded to 2 significant figures must be 10, because rounding it to 1 would be much too small.
Note
Past paper questions have also required candidates to round to a given number of decimal places, or to the nearest 10 or 1000. You should also ensure that you are able to do this.
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Past paper questions
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• 2014 P2 Q1 (nearest 10) • 2014 Paper 2 Q7 (with volume) • 2015 Paper 2 Q6 (with volume) • 2016 Paper 2 Q7 (with volume) • 2017 Specimen P2 Q6 (with volume) • 2017 Paper 2 Q6 (with volume) • 2018 Paper 2 Q7 (with volume) • 2019 Paper 2 Q6 (with quadratics) • 2019 Paper 2 Q8 (with volume) • 2021 Paper 2 Q11 (with volume) • 2021 Paper 2 Q15 (with quadratics) • 2022 Paper 2 Q2 (nearest 1000) • 2022 Paper 2 Q7 (with quadratics) • 2023 P2 Q3 (with scientific notation) • 2023 P2 Q14 (with quadratics) • 2024 Paper 2 Q1 (with percentages) • 2024 Paper 2 Q8 (with quadratics) |
Other great resources
| Video - Larbert High School |
| Notes - BBC Bitesize |
| Notes - Maths4Scotland |
| Videos - Mr Thomas Maths |
| Worked examples - Maths Mutt |
| Worksheet - Corbett Maths |
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