National 5 Maths
Rounding

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Course content

• Rounding to a given number of significant figures or decimal places.

Textbook page references

• Zeta National 5+ Maths pp.1-4
• TeeJay Maths N4 Book 2 page 28
• Leckie National 5 Maths pp.84-88

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.

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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

Recommended student book

Zeta Maths: National 5 Maths Textbook 
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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

• 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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