Skip to content
Teachers
Go to pupils
Choose exam board for KS4 Biology
Choose exam board for KS4 Chemistry
Choose exam board for KS4 Combined science
Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Physics
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

Guidance

About us

Multiples of 10 involving negative exponents

Download all resources
Previous lesson
Next lesson
Skip to lesson content
Share lesson with pupils

Lesson details

Learning outcome

I can write any integer in a range of forms.

Key learning points

  1. A positive exponent tells you how many identical values must be multiplied together.
  2. Dividing by 10^n is the same as multiplying by its reciprocal.
  3. A negative exponent tells you how many reciprocals of the base must be multiplied together.
  4. a^(−3) = 1/a^3

Keywords

  • Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

Common misconception

A negative exponent implies that the entire value is negative.

Refer back to the table showing the structure of how the negative exponents occur and highlight that none of the decimal values are negative.

Teacher tip

Ensure that you have place value grids accessible with the exponents of 10 included.

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
 except where otherwise stated. See Oak's terms & conditions
 (Collection 2).

Lesson video

Skip lesson video

Loading...

Prior knowledge starter quiz

Download starter quiz questions (PDF)

6 Questions

Q1.
A prime number is an integer greater than one with exactly factors.

Correct Answer: 2, two

Q2.
Which of the following products only use prime numbers?

Correct answer: 2 × 2 × 13
2 × 6 × 13
2 × 9 × 13
Correct answer: 2 × 3 × 5 × 17

Q3.
Write 300 as a product of its prime factors.

4 × 3 × 25
Correct answer: 2² × 3 × 5²
4 × 3 × 5²
2² × 3 × 25
2² × 3 × 5

Q4.
Use the fact that 60 = 2² × 3 × 5 to write 300 as a product of its prime factors.

2² × 3² × 5
Correct answer: 2² × 3 × 5²
2² × 3² × 5²
2 × 3 × 5²

Q5.
Use the fact that 60 = 2² × 3 × 5 to write 30 as a product of its prime factors.

2² × 3 × 5 ÷ 2
Correct answer: 2 × 3 × 5
2² × 5
2 × 3 × 5²

Q6.
If 52 = 2² × 13 and 175 = 5² × 7, which of the following is the most useful arrangement to calculate 175 × 52?

2 × 2 × 13 × 5 × 5 × 7
2 × 13 × 2 × 5 × 5 × 7
Correct answer: 2 × 5 × 2 × 5 × 13 × 7
2 × 7 × 2 × 5 × 13 × 5

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
A number written in exponential form represents a repeated ...

addition
division
Correct answer: multiplication
subtraction

Q2.
Match each fraction to its equivalent exponential form.

Correct Answer:$${1}\over{10}$$,$$10^{-1}$$

$$10^{-1}$$

Correct Answer:$${1}\over{100}$$,$$10^{-2}$$

$$10^{-2}$$

Correct Answer:$${1}\over{1000}$$,$$10^{-3}$$

$$10^{-3}$$

Correct Answer:$${1}\over{10 000}$$,$$10^{-4}$$

$$10^{-4}$$

Correct Answer:$${1}\over{100 000}$$,$$10^{-5}$$

$$10^{-5}$$

Correct Answer:$${1}\over{1 000 000}$$,$$10^{-6}$$

$$10^{-6}$$

Q3.
Match each decimal to its equivalent exponential form.

Correct Answer:$$0.002$$,$$2\times10^{-3}$$

$$2\times10^{-3}$$

Correct Answer:$$0.00004$$,$$4\times10^{-5}$$

$$4\times10^{-5}$$

Correct Answer:$$0.2$$,$$2\times10^{-1}$$

$$2\times10^{-1}$$

Correct Answer:$$0.005$$,$$5\times10^{-3}$$

$$5\times10^{-3}$$

Correct Answer:$$0.000005$$,$$5\times10^{-6}$$

$$5\times10^{-6}$$

Correct Answer:$$0.0004$$,$$4\times10^{-4}$$

$$4\times10^{-4}$$

Q4.
$$3\times10^{-2}+2\times10^{-5}+8\times10^{-6}$$ represents the number

Correct Answer: 0.030028, 0.030 028

Q5.
Which of the following is not an alternative way of writing 2400?

$$24\times10^2$$
$$24 000\div10$$
Correct answer: $$240 000\div10^3$$
$$2.4\times10^3$$
$${{240}\over{10}}\times10^2$$

Q6.
Which of the following is not an alternative way of writing 12 000?

Correct answer: $$1.2\times10^3$$
$${{1200}\over{10^2}}\times10^3$$
$$120 000\times10^{-1}$$
$$1.2\times10^4$$
Correct answer: $${{120}\over{10^3}}\times10^4$$

To help you plan your 9 maths lesson on: Multiples of 10 involving negative exponents, download all teaching resources for free and adapt to suit your pupils' needs...