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.

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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