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

An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

Checking and securing understanding of multiples of 10

Maths

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

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

Using the Gattegno chart or otherwise, work out which of the following calculations equate to 24.

Using the Gattegno chart or otherwise, match each calculation to its correct answer.

Using the associative law to partition 4000 and 2000 into powers of 10, find the calculations that are equivalent to 4000 × 2000.

Which of the following calculations are equivalent to $$5000\times5000$$?

Which of the following calculations are equivalent to $$6.5\times2.4$$?

Which of the following calculations are equivalent to $$4.5\times0.03$$?

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

Fill in the missing exponent of $$8\times8\times8\times8\times8 = 8^\square$$

$$8\times8\times8\times8\times8\times8\times8 = 8^\square$$

$$4\times4\times4\times4\times4\times4\times4\times4= 4^\square$$

$$5\times5\times5\times5\times5= 5^\square$$

Match each missing exponent with the correct statement.

Match each number written in exponent form with its value.

Without a calculator, work out 3.4 × 1.5.

Starter Quiz

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