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

Multiples of 10 involving negative exponents

Maths

Checking and securing understanding of multiples of 10

Checking and further securing understanding of the commutative law

Writing large numbers in standard form

Writing small 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

A number written in exponential form represents a repeated ...

Match each fraction to its equivalent exponential form.

Match each decimal to its equivalent exponential form.

$$3\times10^{-2}+2\times10^{-5}+8\times10^{-6}$$ represents the number {{ }}

Which of the following is **not** an alternative way of writing 2400?

Which of the following is **not** an alternative way of writing 12 000?

A prime number is an integer greater than one with exactly {{ }} factors. 

Which of the following products only use prime numbers?

Write 300 as a product of its prime factors.

Use the fact that 60 = 2² × 3 × 5 to write 300 as a product of its prime factors.

Use the fact that 60 = 2² × 3 × 5 to write 30 as a product of its prime factors.

If 52 = 2² × 13 and 175 = 5² × 7, which of the following is the most useful arrangement to calculate 175 × 52?

Multiples of 10 involving negative exponents

Lesson outcome