Number: Fractions, Percentages and Standard Form

Three ways to write a number

This module brings together three number skills that examiners test again and again. First, fractions, decimals and percentages are three ways of writing the same value, so 1/2 is the same as 0.5 and the same as 50 per cent, and being able to switch between them at will is the key to the topic. Second, a percentage can act on an amount, so you can find a percentage of a quantity, such as a discount or a share. Third, standard form is a short way of writing very large or very small numbers as a value between 1 and 10 multiplied by a power of ten, which keeps long numbers manageable. This module covers converting between the three forms, finding a percentage of an amount, and writing numbers in standard form, and every calculation here has been checked.

Number words

Learn what each of these means before you use it.

Ordinary numbers against standard form

Standard form is just a shorter way of writing the same value.

How to convert between the forms

Fractions, decimals and percentages are three ways of writing the same value, and moving between them is the heart of this topic. To turn a fraction into a decimal, divide the top number by the bottom number. To turn a decimal into a percentage, multiply it by one hundred. To turn a percentage into a fraction, write it over one hundred and cancel down. It pays to know the common ones instantly rather than working them out each time. When a question mixes the three forms, change them all into the same form first, and comparing them becomes straightforward.

Match the fraction to its percentage

A percentage of an amount

Work out 25 per cent of 80. A useful shortcut is that 25 per cent is one quarter, so divide 80 by 4.

Which fraction is 50 per cent?

Which one of these fractions is equal to 50 per cent?

• one half
• one quarter
• one fifth
• three quarters

Into standard form

To write 45000 in standard form you write 4.5 times ten to the power of n. Work out the value of n.

True about number

Select the TWO statements that are true.

• Three quarters is equal to 75 per cent
• To change a decimal into a percentage you multiply by one hundred
• One half is equal to 25 per cent
• Standard form is used to make small numbers longer to write

Complete the number facts

A percentage written as a fraction has a denominator of _____. The fraction one quarter is equal to _____ per cent. Standard form writes a number as a value between 1 and 10 times a power of _____. Writing 3000 in standard form gives 3 times ten to the power of _____.

Order by size

Put these fractions in order of size, smallest first.

• 1/10
• 1/4
• 1/2
• 3/4

Spot the true number facts

Tap the TWO statements that are true.

• One half is equal to 50 per cent
• Three quarters is equal to 75 per cent
• One quarter is larger than one half
• Standard form makes large numbers longer to write

Choose the method

Read each case and choose the best response, with a reason.

• You need to find 10 per cent of 250. What is the quickest correct method?
• You must write 6000 in standard form. Which is correct?
• You want to compare the fraction 3/5 with 55 per cent to see which is larger. What is the best first step?

Explain how the three forms fit

A friend finds fractions, percentages and standard form confusing and asks how they fit together. Explain how to work with fractions, percentages and standard form.

• Explain that fractions, decimals and percentages are three ways of writing the same value
• Explain how to change a fraction into a percentage
• Explain how to find a percentage of an amount, with a worked example
• Explain what standard form is and why it is useful
• Finish by explaining how to compare a fraction and a percentage fairly