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Powers of 10 and standard form - Teacher Slides.pptx
The lesson slides with the teacher's notes on each slide, and every question and mark scheme built in. Built from the lesson script on 28 September 2026.
EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Powers of 10 and standard form
Number
Lesson 6 of 7
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Last Lesson and Before
Number
Lesson 6 of 7
Answer each one, then check.
1
What is 10³?
2
Last lesson: what is 10⁻²?
3
Work out 4.5 × 100.
4
Write 10⁵ × 10³ as a single power of 10.
5
Last lesson: what is 5⁰?
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Last Lesson and Before - Answers
Number
Lesson 6 of 7
1
What is 10³?
1000
2
Last lesson: what is 10⁻²?
1/100 = 0.01
3
Work out 4.5 × 100.
450
4
Write 10⁵ × 10³ as a single power of 10.
10⁸
5
Last lesson: what is 5⁰?
1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Learning Objectives
Number
Lesson 6 of 7
1
Write positive and negative powers of 10 as ordinary numbers.
2
Use metric prefixes such as kilo, mega, milli and micro.
3
Write numbers in standard form, and change them back.
4
Multiply and divide numbers in standard form.
5
Add and subtract numbers in standard form, and use a calculator with them.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Powers of 10
Number
Lesson 6 of 7
Multiplying by 10ⁿ moves every digit n places.
Positive powers
10⁶ = 1 000 000. 3.2 × 10⁴ = 32 000: the digits move 4 places left.
Negative powers
10⁻³ = 1/1000 = 0.001. 3.2 × 10⁻⁴ = 0.000 32: the digits move 4 places right.
Multiplying powers of 10
10⁵ × 10³ = 10⁸. Add the indices, as for any base.
Dividing powers of 10
10⁵ ÷ 10⁸ = 10⁻³. Subtract the indices.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Metric Prefixes
Number
Lesson 6 of 7
Each prefix stands for a power of 10.
Prefix
Symbol
Power of 10
Example
giga
G
10⁹
1 gigabyte = 1 000 000 000 bytes
mega
M
10⁶
1 megawatt = 1 000 000 watts
kilo
k
10³
1 kilometre = 1000 metres
milli
m
10⁻³
1 millimetre = 0.001 metres
micro
μ
10⁻⁶
1 micrometre = 0.000 001 metres
nano
n
10⁻⁹
1 nanosecond = 0.000 000 001 seconds
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
What Is Standard Form?
Number
Lesson 6 of 7
A number in standard form is written as A × 10ⁿ, where 1 ≤ A < 10 and n is a whole number.
The first part
A number from 1 up to (but not including) 10: one non-zero digit before the decimal point.
The power
How many places the digits have moved. Positive for big numbers, negative for small numbers (less than 1).
Big numbers
45 000 = 4.5 × 10⁴.
Small numbers
0.0072 = 7.2 × 10⁻³.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Writing Numbers in Standard Form
Number
Lesson 6 of 7
Number
Standard form
How
45 000
4.5 × 10⁴
4.5 moved 4 places left
3 080 000
3.08 × 10⁶
3.08 moved 6 places left
0.0072
7.2 × 10⁻³
7.2 moved 3 places right
0.000 050 1
5.01 × 10⁻⁵
5.01 moved 5 places right
38 × 10⁴
3.8 × 10⁵
38 = 3.8 × 10¹, so add 1 to the power
0.6 × 10⁻²
6 × 10⁻³
0.6 = 6 × 10⁻¹, so subtract 1 from the power
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Is It in Standard Form?
Number
Lesson 6 of 7
YES
• 3.2 × 10⁵
• 9 × 10⁻⁴
• 1.07 × 10¹²
• 5 × 10⁰, which is 5
NO - AND WHY
• 32 × 10⁴: 32 is not less than 10.
• 0.9 × 10⁻³: 0.9 is less than 1.
• 1.07 × 5¹²: it must be a power of 10.
• 4.5 × 10^(2.5): the power must be a whole number.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
From Tiny to Huge
Number
Lesson 6 of 7
Standard form lets the whole universe fit on one scale.
10⁻¹⁰ M
10²¹ M
An atom
About 1 × 10⁻¹⁰ m across
A red blood cell
About 8 × 10⁻⁶ m across
A person
About 1.7 × 10⁰ m (1.7 m) tall
The Earth
About 1.3 × 10⁷ m across
Our galaxy
About 1 × 10²¹ m across
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
PART TWO
Calculating in Standard Form
Deal with the numbers and the powers separately.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Multiplying in Standard Form
Number
Lesson 6 of 7
Work out (3 × 10⁵) × (6 × 10⁻²). Give your answer in standard form.
1
Multiply the numbers
3 × 6 = 18
2
Multiply the powers: add the indices
10⁵ × 10⁻² = 10³
3
Put them together
18 × 10³
4
18 is not between 1 and 10: 18 = 1.8 × 10¹
1.8 × 10¹ × 10³
ANSWER
1.8 × 10⁴
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Dividing in Standard Form
Number
Lesson 6 of 7
Work out (4.8 × 10⁶) ÷ (1.2 × 10⁻³). Give your answer in standard form.
1
Divide the numbers
4.8 ÷ 1.2 = 4
2
Divide the powers: subtract the indices
10⁶ ÷ 10⁻³ = 10⁶⁻⁽⁻³⁾ = 10⁹
3
Put them together
4 × 10⁹
ANSWER
4 × 10⁹
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Adding in Standard Form
Number
Lesson 6 of 7
Work out (4.5 × 10⁴) + (3 × 10³). Give your answer in standard form.
1
The powers are different, so write both as ordinary numbers
45 000 and 3000
2
Add
45 000 + 3000 = 48 000
3
Write the answer in standard form
4.8 × 10⁴
ANSWER
4.8 × 10⁴
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Standard Form on a Calculator
Number
Lesson 6 of 7
Calculators have a key for entering powers of 10.
The key
Look for the "×10 to the x" key (EXP on some models). To enter 3.2 × 10⁻⁵, press 3.2, then that key, then −5.
Reading the display
A display like 1.8E4 means 1.8 × 10⁴. Always write the answer with × 10 and a power.
Brackets
When dividing by a number in standard form, put it in brackets, or use the power-of-10 key.
Check
Estimate first: is the power of 10 about right?
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Number
Lesson 6 of 7
CASE STUDY
How Long Does Sunlight Take to Reach Us?
The Sun is about 1.5 × 10⁸ km from the Earth, and light travels at about 3 × 10⁵ km per second. Time = distance ÷ speed = (1.5 × 10⁸) ÷ (3 × 10⁵) = 0.5 × 10³ = 5 × 10² seconds: about 500 seconds, or 8 minutes 20 seconds. So when you look at the Sun, you are seeing it as it was more than 8 minutes ago. Standard form turns a calculation with 17 digits into two small divisions.
1.5 × 10⁸ km
Distance from the Earth to the Sun
5 × 10² s
Time for sunlight to reach us - about 8 minutes
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Key Terms
Number
Lesson 6 of 7
Standard form
A number written as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer.
Power of 10
10 multiplied by itself a number of times, e.g. 10³ = 1000.
Prefix
Letters in front of a unit that stand for a power of 10, e.g. kilo = 10³.
Ordinary number
A number written out in full, without powers of 10.
Integer
A whole number, positive, negative or zero.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Number
Lesson 6 of 7
YOUR TASK
Space and Cells
12 minutes
Use standard form for each question, without a calculator. (a) Write 6 000 000 000 000 in standard form. (b) A bacterium is 2 × 10⁻⁶ m long. How many would fit end to end along 1 cm (1 × 10⁻² m)? (c) Put in order, smallest first: 3.1 × 10⁴, 2.9 × 10⁵, 31 000, 0.3 × 10⁵. (d) Work out (2.5 × 10³) × (4 × 10⁶).
1
Write each number in standard form first.
2
Deal with the numbers and the powers separately.
3
Check the first part is between 1 and 10.
WHAT A GOOD ANSWER SHOWS
(a) 6 × 10¹². (b) (1 × 10⁻²) ÷ (2 × 10⁻⁶) = 0.5 × 10⁴ = 5 × 10³ = 5000. (c) 0.3 × 10⁵ (30 000), then 3.1 × 10⁴ and 31 000 (equal), then 2.9 × 10⁵. (d) 10 × 10⁹ = 1 × 10¹⁰.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can I...?
Number
Lesson 6 of 7
Write powers of 10 as ordinary numbers.
Use metric prefixes.
Write a large number in standard form.
Write a small number in standard form.
Change standard form back to an ordinary number.
Multiply and divide in standard form.
Add and subtract in standard form.
Use the power-of-10 key on a calculator.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Summary & Exam Focus
Standard form: A × 10ⁿ with 1 ≤ A < 10.
Positive powers for big numbers, negative powers for numbers less than 1.
Multiply or divide the numbers and the powers separately, then adjust.
To add or subtract, make the powers match or use ordinary numbers.
EXAM FOCUS
Work out (5 × 10⁻³) × (7 × 10⁸). Give your answer in standard form. (2 marks)
After multiplying or dividing, check the first number is between 1 and 10. 35 × 10⁵ is a correct value but not standard form, and loses the accuracy mark.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Standard Form
Number
Lesson 6 of 7
Answer all questions. Show your working. Questions 1 to 5 are non-calculator. · 25 minutes
Question 1 · 1 mark · Non-calculator
Write 0.000 604 in standard form.
Question 2 · 1 mark · Non-calculator
Write 7.3 × 10⁵ as an ordinary number.
Question 3 · 2 marks · Non-calculator
Work out (5 × 10⁻³) × (7 × 10⁸). Give your answer in standard form.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Standard Form (cont.)
Number
Lesson 6 of 7
Question 4 · 2 marks · Non-calculator
Work out (8.4 × 10⁷) ÷ (2.1 × 10⁻²). Give your answer in standard form.
Question 5 · 2 marks · Non-calculator
Write these numbers in order of size, starting with the smallest. 4.1 × 10⁻³, 0.0039, 42 × 10⁻⁴, 0.4 × 10⁻²
Question 6 · 3 marks · Calculator
The mass of one atom of gold is 3.27 × 10⁻²² grams. How many atoms of gold are there in 1 kilogram of gold? Give your answer in standard…
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · 1 mark · Non-calculator
Number
Lesson 6 of 7
“
Write 0.000 604 in standard form.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 1 mark, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · mark scheme
Number
Lesson 6 of 7
1 mark available. Award a mark for each point made.
6.04 × 10⁻⁴
B1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · 1 mark · Non-calculator
Number
Lesson 6 of 7
“
Write 7.3 × 10⁵ as an ordinary number.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 1 mark, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · mark scheme
Number
Lesson 6 of 7
1 mark available. Award a mark for each point made.
730 000
B1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · 2 marks · Non-calculator
Number
Lesson 6 of 7
“
Work out (5 × 10⁻³) × (7 × 10⁸). Give your answer in standard form.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · mark scheme
Number
Lesson 6 of 7
2 marks available. Award a mark for each point made.
35 × 10⁵ or 3 500 000 seen
M1
3.5 × 10⁶
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · 2 marks · Non-calculator
Number
Lesson 6 of 7
“
Work out (8.4 × 10⁷) ÷ (2.1 × 10⁻²). Give your answer in standard form.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · mark scheme
Number
Lesson 6 of 7
2 marks available. Award a mark for each point made.
4 seen, or 10⁹ seen
M1
4 × 10⁹
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · 2 marks · Non-calculator
Number
Lesson 6 of 7
“
Write these numbers in order of size, starting with the smallest. 4.1 × 10⁻³, 0.0039, 42 × 10⁻⁴, 0.4 × 10⁻²
HOW TO ANSWER IT
Command word: Non-calculator. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · mark scheme
Number
Lesson 6 of 7
2 marks available. Award a mark for each point made.
All four in the correct order
B2
At least three converted correctly to the same form, or one pair out of order
B1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · 3 marks · Calculator
Number
Lesson 6 of 7
“
The mass of one atom of gold is 3.27 × 10⁻²² grams. How many atoms of gold are there in 1 kilogram of gold? Give your answer in standard form, correct to 3 significant figures.
HOW TO ANSWER IT
Command word: Calculator. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · mark scheme
Number
Lesson 6 of 7
3 marks available. Award a mark for each point made.
1 kg = 1000 g used
P1
1000 ÷ (3.27 × 10⁻²²)
P1
3.06 × 10²⁴
A1
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