New

Year 9

Problem solving with standard form

I can use my knowledge of standard form to solve problems.

Download all resources

Share activities with pupils

New

Year 9

Problem solving with standard form

I can use my knowledge of standard form to solve problems.

Download all resources

Share activities with pupils

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

View new resources

Slide deck

Download slide deck

Skip slide deck

Lesson details

Key learning points

Standard form is used frequently in Science.
The exponent can tell you how large the number will be.
The exponent can tell you how small the number will be.

Keywords

Standard form - Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).
Associative law - The associative law states that a repeated application of the operation produces the same result regardless of how pairs of values are grouped. We can group using brackets.

Common misconception

Pupils can incorrectly write a number in standard form or use a number in incorrect standard form whereby the number A does not satisfy 1 ≤ A < 10 or pupils use division of positive powers of 10.

Standard form represents a multiplicative relationship, so there should always be a multiplication. Embedding the understanding that negative exponents refer to 1/10^n is important. Using the place value chart with fractional and exponent form helps.

To help you plan your year 9 maths lesson on: Problem solving with standard form, download all teaching resources for free and adapt to suit your pupils' needs...

Encourage pupils to write out the number of multiplications of 10 and 1/10 which can then simplify to 1. This layer of working out reinforces pupil understanding of the principles behind adding to the exponent when A is too big, or subtracting from the exponent when A is too small.

Teacher tip

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

Worksheet

Download worksheet

Skip worksheet

Starter quiz

Download starter quiz

6 Questions

Q1.

These are all examples of numbers written in standard :

3.1 \times 10^{2}

7.98 \times 10^{- 2}

and

2.39 \times 10^{6}

Correct Answer: form

Q2.

Which of the following inequalities is incorrect?

6.54 \times 10^{4} < 2.4 \times 10^{6}

Correct answer:

3.42 \times 10^{4} < 3.4 \times 10^{4}

1.92 \times 10^{2} < 1.98 \times 10^{2}

2.08 \times 10^{3} < 3.4 \times 10^{4}

2.607 \times 10^{5} < 1.04 \times 10^{8}

Q3.

Starting with the smallest, put these numbers written in standard form in order of size.

1 -

9.4 \times 10^{2}

2 -

5.3 \times 10^{3}

3 -

7 \times 10^{3}

4 -

2.07 \times 10^{4}

5 -

1.87 \times 10^{5}

Q4.

Which of the following inequalities is incorrect?

6.54 \times 10^{- 4} < 2.4 \times 10^{- 2}

3.56 \times 10^{- 3} < 5.07 \times 10^{- 2}

7.56 \times 10^{- 2} < 4.2 \times 10^{- 1}

Correct answer:

2.72 \times 10^{- 4} < 2.8 \times 10^{- 6}

1.23 \times 10^{- 4} < 1.023 \times 10^{- 2}

Q5.

Starting with the smallest, put these numbers written in standard form in order of size.

1 -

9.4 \times 10^{- 5}

2 -

1.8 \times 10^{- 4}

3 -

9 \times 10^{- 4}

4 -

3.01 \times 10^{- 3}

5 -

2.3 \times 10^{- 2}

Q6.

Starting with the smallest, put these numbers in order of size.

1 -

32 \times 0.001

2 -

3.2 \times 10^{- 1}

3 -

32 \div 10

4 -

3.2 \times 10^{3}

5 -

320 \times \frac{1}{10^{- 2}}

Exit quiz

Download exit quiz

6 Questions

Q1.

Why is

46 \times 10^{- 20}

not written in standard form?

The exponent cannot be negative

It should be ÷ and not ×

Correct answer: 46 is not greater than or equal to 1 and less than 10

An exponent cannot be over 10

Q2.

Which of the following are not written in standard form?

4.6 \times 10^{2}

Correct answer:

0.15 \times 10^{- 2}

2 \times 10^{- 12}

Correct answer:

10.4 \times 10^{3}

5.006 \times 10^{8}

Q3.

Jacob writes the number

450 \times 10^{3}

in standard form. What should Jacob write for the exponent?

Correct Answer: 5, five

Q4.

Laura writes the number

0.087 \times 10^{6}

in standard form. What should Laura write for the exponent?

Correct Answer: 4, four

Q5.

The width of a human hair is

8 \times 10^{- 5}

metres. The width of 1000 hairs in centimetres is cm.

Correct Answer: 8, 8cm, 8 cm

Q6.

The population of the world in 2024 is roughly 8 billion. The population of Europe is roughly 740 million. To the nearest integer, the population of the world is times bigger than Europe.

Correct Answer: 11, eleven, 11 times, eleven times

Problem solving with standard form

Problem solving with standard form

These resources will be removed by end of Summer Term 2025.

Slide deck

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Starter quiz

6 Questions

Exit quiz

6 Questions