Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).

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.

Problem solving with standard form

Maths

The conditions for standard form mean that pupils have explored how different powers of 10 can be written. In this unit, this understanding is generalised and the index laws formalised. 

In the prior unit, pupils learnt how to factorise multiples of 10 in order to simplify calculations. This understanding is built on in this unit as values are converted to meet the conditions for standard form. 

Standard form

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

Why is $${46}\times{10}^{-20}$$ not written in standard form?

Which of the following are not written in standard form?

Jacob writes the number $$450\times{10}^{3}$$ in standard form. What should Jacob write for the exponent? 

Laura writes the number $$0.087\times{10}^{6}$$ in standard form. What should Laura write for the exponent? 

 The width of a human hair is $${8}\times{10}^{-5}$$ metres. The width of 1000 hairs in centimetres is {{ }} cm.

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.

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

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

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

Which of the following inequalities is **incorrect**?

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

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

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

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

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

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

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

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