When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

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.

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

Writing small numbers in standard form

Maths

Checking and securing understanding of multiples of 10

Checking and further securing understanding of the commutative law

Multiples of 10 involving negative exponents

Writing large numbers in standard form

Ordering numbers in standard form

Problem solving with standard form

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. 

In this unit pupils learn to recognise, interpret and write in standard form. Pupils then extend this knowledge so that they can order numbers written in standard form.

Standard form

Standard form follows this convention:  $$A \times 10^B$$ and $$1 ≤ A < 10$$ and $$B$$ is an {{ }}.

Which of the following are written in standard form?

Use a place value grid to write $$0.00506$$ in standard form.

$${4.08}\times10^{-4}$$ as an ordinary number is {{ }}.

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

{{ }} form follows this convention: $$A \times 10^B$$ and $$1 ≤ A < 10$$ and $$B$$ is an integer.

$${2.45}\times10^{6}$$ as an ordinary number is {{}}.

What should go in the box to make this statement correct? $$240 000 000 000 000 = 2.4 \square$$

Starter Quiz

form follows this convention: $$A \times 10^B$$ and $$1 ≤ A < 10$$ and $$B$$ is an integer.