Fractions, Decimals And Percentages

FRACTIONS, DECIMALS AND PERCENTAGES

(See also the notes on recurring decimals, which can be a bit trickier.)

We often use fractions, decimals and percentages interchangeably. We might say `a half` or `0.5` or `50%` - these mean exactly the same thing and it is helpful to recognise similar equivalents:

3/4, 0.75, 75%

1/10, 0.1, 10%

1/4, 0.25, 25%

and so on.

Some are harder to remember and it can be helpful to know how to convert fractions to decimals to percentages.

Suppose we think about the first example in the list - 3/4, 0.75, 75%. How do we show that these are equivalent?

Fraction to decimal

To convert a fraction to a decimal, simply do the division:

3/4. 4 into 3 gives 0 as the first number (4 won`t go into 3)

7 as the second number (4 goes into 30 7 times, with remainder 2)

5 as the third number (4 goes into 20 5 times, with remainder 0)

= 0.75

(NB This is just ordinary division but hard to show on the site).

Fraction to percentage

This is done in almost exactly the same way but it is no longer 4 into 3, but 4 into 300. So instead of 0.75 we get 75%.

Decimal to percentage

The easiest - just multiply the decimal by 100. Equivalently, move the decimal point two places to the right:

0.75 = 75%

Decimal to fraction

Write the decimal as the decimal divided by 1:

0.75 = 0.75/1

Now look for a way of converting the 0.75 to a whole number. You could just multiply it by 4 if you spot that 0.75x4=3. But if not, just multiply by 100. We now need to multiply the denominator by 100 too so we get

0.75/1 = 75/100.

Now reduce this fraction to its simplest form to get 3/4.

(NB If the decimal is recurring a different approach is needed. See the separate note on recurring decimals.)

Percentage to fraction

Write the percentage as a fraction out of 100 ie

75% = 75/100

and reduce as before to get 3/4.

Percentage to decimal

Divide by 100 or equivalently move the decimal point two places to the left:

75% = 0.75

Questions

Q1 Write 76%, 0.7, 3/4 in descending order.

Q2 In the following list, draw a circle around each number that has the same value as 1/4:

40% 25% 0.14 2/8 0.4

Q3 Write 32%, 1/3, 0.3 in ascending order

Q4 Cheryl scored 60 marks out of 80 in a test. Express Cheryl`s score as a percentage. How many more marks would she need to have got to get 80%? How many more would she need to get 0.85, if we express her mark as a decimal?