National 5 Maths
Scientific Notation

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Page sections

• Topic content
• Textbook page numbers
• Key ideas
• Worked examples
• Past paper questions
• Worksheets
• Notes and videos

Topic content

• Convert to and from scientific notation (positive or negative powers)
• Calculations using scientific notation.

Textbook page numbers

• Zeta National 5+ Maths pp.23-26
• TeeJay Maths N5 Book 4+ pp.66-71
• Leckie National 5 Maths pp.22-24

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Key ideas

• "Scientific notation" is also called "standard form".
• We use powers of 10 to express very large or very small numbers in scientific notation.
• Multiplying by a positive power of 10 moves the decimal point to the right.
• Dividing by a positive power of 10 moves the decimal point to the left.

Powers of 10

10¹ = 10
10² = 100
10³ = 1000
10⁴ = 10 000
10⁵ = 100 000
etc.

Large numbers

Multiplication by a positive power of 10 moves the decimal point to the right. For example: 1.23 \(\times\) 10⁴ = 12 300.

Small numbers

Division by a positive power of 10 moves the decimal point to the left. For example: 9.87 ÷ 10³ = 0.00987.

Dividing by 10³ is the same as multiplying by 10^–3. Please study the index laws if this isn't obvious to you.

So we can also write 0.00987 as 9.87 \(\times\) 10^–3. Scientific notation always uses a \(\times\) sign, not \(\div.\)

Note

In \(a\times 10^n\), the number \(a\) is called the "mantissa" and \(n\) is the "exponent" (or index, or power).

We must always make sure that 1 ≤ \(a\) < 10, so that there is a single non-zero digit before the decimal point.

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Example 1 (calculator)

Express 51 600 000 in scientific notation.

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Example 2 (non-calculator)

Express 0.00007081 in standard form.

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Example 3 (non-calculator)

Evaluate (4 \(\times\) 10¹⁴) ÷ (8 \(\times\) 10⁶). Express your answer in scientific notation.

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Example 4 (calculator)

In the year 2015, there were estimated to be 7.34 \(\times\) 10⁹ people and 3.04 \(\times\) 10¹² trees in the world. Calculate the number of trees per person in 2015. Express your answer correct to 2 significant figures.

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Example 5 (calculator)

The average adult has approximately 7.6 \(\times\) 10⁶ white blood cells per millilitre of blood. On average, an adult has 5.2 litres of blood. Calculate the average number of white blood cells in an adult body. Express your answer in scientific notation, correct to 1 significant figure.

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Example 6 (calculator)

SQA National 5 Maths 2016 P2 Q2

A pollen sample weighs 12 grams and contains 1.5 \(\times\) 10⁹ pollen grains. Calculate the weight of one pollen grain in grams. Give your answer in scientific notation.

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Example 7 (calculator)

SQA National 5 Maths 2019 P2 Q4

A sesame seed weighs 3.6 \(\times\) 10^–6 kilograms. The weight of a poppy seed is 8% of the weight of a sesame seed. Calculate the weight of a poppy seed in kilograms. Give your answer in scientific notation.

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Example 8 (calculator)

SQA National 5 Maths 2021 P2 Q2

Light travels at 3 \(\times\) 10⁸ metres per second. A star is 4.2 \(\times\) 10¹⁷ metres away from Earth. Calculate the number of seconds it takes for light from this star to reach Earth. Give your answer in scientific notation.

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Example 9 (calculator)

SQA National 5 Maths 2023 P2 Q2

The mass of a helium atom is 6.64 \(\times\) 10^–24 grams. A flask contains 300 grams of helium. Calculate the number of helium atoms in this flask. Give your answer in scientific notation, correct to 3 significant figures.

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Example 10 (calculator)

SQA National 5 Maths 2024 P2 Q2

An ant colony occupies an area of 250 hectares. There is an average of 1.22 \(\times\) 10⁶ ants per hectare. Calculate the number of ants in the colony. Give your answer in scientific notation.

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Example 11 (calculator)

SQA National 5 Maths 2025 P2 Q3

The mass of one atom of gold is 3.27 \(\times\) 10^–22 grams. The mass of one atom of carbon is 6.1% of the mass of an atom of gold. Calculate the mass of one atom of carbon. Give your answer in scientific notation.

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Buy N5 Maths practice papers

Zeta: Five Practice Papers   TOP CHOICE
CGP: N5 Maths Exam Practice 
Leckie: Revision and Practice 
Hodder: N5 Maths Practice Papers 

Past paper questions

• All past paper questions by topic

• 2015 Paper 2 Q6 (with rounding) • 2016 Paper 2 Q2 • 2017 Specimen Paper 2 Q2 • 2018 P2 Q11 (with percentages) • 2019 Paper 2 Q4 • 2021 Paper 2 Q2 • 2023 Paper 2 Q2 • 2024 Paper 2 Q2 • 2025 Paper 2 Q3

Standard Grade: Credit (1986–2013) • Exam questions and answers

Buy our favourite N5 textbook

Zeta National 5+ Maths
Clear and comprehensive.
Progressive exercises.
Includes answers.
Buy from Zeta Press 

Worksheets

Maths.scot worksheet • Scientific notation (Answers)

D R Turnbull - worksheets 1. Scientific notation (with answers) 2. Calculations (with answers) 3. Speed calculations (with answers)

Corbettmaths worksheet 1. Standard Form (Answers)

National5Maths.co.uk worksheets 1. Positive exponents (with answers) 2. Exam style questions (no answers)

Maths Hunter worksheet • Practice questions (no answers)

Larkhall Academy exercises • Pages 17-20 Ex 1-3 (no answers)

Buy N5 Maths revision guides

How to Pass N5 Maths    TOP CHOICE
BrightRED: N5 Maths Study Guide 
CGP: N5 Maths Revision Guide 

Notes and videos

Videos - Maths180.com Scroll down, below the indices videos.

Video - Math Antics American, but relevant.

Video - YouKenMaths Standard Grade 2009 Paper 2 Q1

Video - Larbert High School

Notes - Maths4Scotland

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