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

Ordering 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

Writing small 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

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

$${9.88}\times10^{2} <{2.5}\times10^{3}$$

$${1.8}\times10^{8} < {2.5}\times10^{8}$$

$${1.45}\times10^{6}<{1.456}\times10^{6}$$

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

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

$${6.7}\times10^{-4}<{1.4}\times10^{-3}$$

$${2.72}\times10^{-1}<{2.8}\times10^{-2}$$

$${8.2}\times10^{-3}<{2.8}\times10^{-2}$$

$${2.72}\times10^{-1}<{2.8}\times10^{-1}$$

$${1.04}\times10^{-6}<{1.045}\times10^{-6}$$

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

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

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

Which of the following are written in standard form?

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

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

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

Ordering numbers in standard form

Lesson outcome