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Ordering numbers in standard form

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Lesson details

Learning outcome

I can compare and order numbers written in a mixture of standard, non-standard and not quite standard form.

Key learning points

  1. It can be easier to compare numbers if they are all in standard form.
  2. If all numbers are in standard form, you can compare the powers of 10
  3. When powers of 10 are the same, you can compare the digits of what remains.

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).

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.

Teacher tip

On MWB, ask pupils to write five different numbers using incorrect standard form, swap MWB and ask pupils to put their peer's numbers in ascending order, showing all working out. Encourage the use of positive and negative exponents. Checking of answers can be done using a calculator.

Licence

This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Numbers written in standard form are written in the form $$A \times 10^B$$ where $$A$$ is ___________.

greater than 1 and less than 10
Correct answer: greater than or equal to 1 and less than 10
greater than or equal to 1 and less than or equal to 10
greater than 1 and less than or equal to 10
an integer

Q2.
Which of the following are written in standard form?

$${2.3}\div10^{2}$$
Correct answer: $${2.08}\times10^{-5}$$
$${0.258}\times10^{-4}$$
$${1.07}\div10^{-2}$$
Correct answer: $${1.0045}\times10^{-3}$$

Q3.
Use a place value grid to write $$0.00026$$ in standard form.

$${2.6}\times10^{-3}$$
$${2}\div10^{-4}$$
$${2.6}\div10^{-3}$$
Correct answer: $${2.6}\times10^{-4}$$
$${2}\times10^{-4}$$

Q4.
Write $$0.000026$$ in standard form.

$${2.6}\times10^{-4}$$
Correct answer: $${2.6}\times10^{-5}$$
$${2.6}\div10^{-5}$$
$${2.6}\times10^{5}$$
$${26}\times10^{-6}$$

Q5.
$${5.23}\times10^{-2}$$ as an ordinary number is .

Correct Answer: 0.0523

Q6.
Match each ordinary number to the equivalent number written in standard form.

Correct Answer:$$0.0033$$,$${3.3}\times10^{-3}$$

$${3.3}\times10^{-3}$$

Correct Answer:$$30 300$$,$${3.03}\times10^{4}$$

$${3.03}\times10^{4}$$

Correct Answer:$$0.00303$$,$${3.03}\times10^{-3}$$

$${3.03}\times10^{-3}$$

Correct Answer:$$33 000$$,$${3.3}\times10^{4}$$

$${3.3}\times10^{4}$$

Correct Answer:$$0.0303$$,$${3.03}\times10^{-2}$$

$${3.03}\times10^{-2}$$

Correct Answer:$$330 000$$,$${3.3}\times10^{5}$$

$${3.3}\times10^{5}$$

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
These are all examples of numbers written in form: $${9.04}\times10^{2}$$, $${2.98}\times10^{-2}$$ and $${1.39}\times10^{8}$$

Correct Answer: standard

Q2.
Which of the following inequalities is incorrect?

$${9.88}\times10^{2} <{2.5}\times10^{3}$$
$${1.8}\times10^{8} < {2.5}\times10^{8}$$
$${3.02}\times10^{3}<{2.5}\times10^{5}$$
Correct answer: $${5.4}\times10^{3}<{5.04}\times10^{3}$$
$${1.45}\times10^{6}<{1.456}\times10^{6}$$

Q3.
Starting with the smallest, put these numbers written in standard form in order of size.

1 - $${8}\times10^{2}$$
2 - $${1.31}\times10^{3}$$
3 - $${2.1}\times10^{4}$$
4 - $${2.2}\times10^{4}$$
5 - $${2.8}\times10^{5}$$

Q4.
Which of the following inequalities is incorrect?

$${6.7}\times10^{-4}<{1.4}\times10^{-3}$$
Correct answer: $${2.72}\times10^{-1}<{2.8}\times10^{-2}$$
$${8.2}\times10^{-3}<{2.8}\times10^{-2}$$
$${2.72}\times10^{-1}<{2.8}\times10^{-1}$$
$${1.04}\times10^{-6}<{1.045}\times10^{-6}$$

Q5.
Starting with the smallest, put these numbers written in standard form in order of size.

1 - $${7.4}\times10^{-6}$$
2 - $${9.4}\times10^{-5}$$
3 - $${2.308}\times10^{-4}$$
4 - $${2.318}\times10^{-4}$$
5 - $${3.23}\times10^{-2}$$

Q6.
Starting with the smallest, put these numbers in order of size.

1 - $${4.6}\times{10}^{-4}$$
2 - $${4.6}\times0.01$$
3 - $${4.6}\times{10}^{-1}$$
4 - $${4.6}\times{10}^2$$
5 - $${4600}\times{{1}\over{10}^{-1}}$$

To help you plan your 9 maths lesson on: Ordering numbers in standard form, download all teaching resources for free and adapt to suit your pupils' needs...