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.

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.

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.

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This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.

These are all examples of numbers written in standard : $${3.1}\times10^{2}$$, $${7.98}\times10^{-2}$$ and $${2.39}\times10^{6}$$

Correct Answer: form

Q2.

Which of the following inequalities is incorrect?

$${6.54}\times10^{4}<{2.4}\times10^{6}$$

Correct answer: $${3.42}\times10^{4}<{3.4}\times10^{4}$$

$${1.92}\times10^{2}<{1.98}\times10^{2}$$

$${2.08}\times10^{3}<{3.4}\times10^{4}$$

$${2.607}\times10^{5}<{1.04}\times10^{8}$$

Q3.

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

1 - $${9.4}\times10^{2}$$

2 - $${5.3}\times10^{3}$$

3 - $${7}\times10^{3}$$

4 - $${2.07}\times10^{4}$$

5 - $${1.87}\times10^{5}$$

Q4.

Which of the following inequalities is incorrect?

$${6.54}\times10^{-4}<{2.4}\times10^{-2}$$

$${3.56}\times10^{-3}<{5.07}\times10^{-2}$$

$${7.56}\times10^{-2}<{4.2}\times10^{-1}$$

Correct answer: $${2.72}\times10^{-4}<{2.8}\times10^{-6}$$

$${1.23}\times10^{-4}<{1.023}\times10^{-2}$$

Q5.

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

1 - $${9.4}\times10^{-5}$$

2 - $${1.8}\times10^{-4}$$

3 - $${9}\times10^{-4}$$

4 - $${3.01}\times10^{-3}$$

5 - $${2.3}\times10^{-2}$$

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 - $${320}\times{{1}\over{10}^{-2}}$$

Exit quiz

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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