## What you need to know

### Fractions Decimals and Percentages

Here we will be going through how to convert between fractions, decimals, and percentages (in all directions).

### Decimals to Percentages

Converting between decimals and percentages is nice and straightforward.

Convert decimal to percentage – multiply by 100 (shift the decimal point right two places).

Convert percentage to decimal – divide by 100 (shift the decimal point left two places).

### Fractions to Decimals

Converting between fractions and decimals is a little more work.

Convert fraction to decimal – treat the fraction like a division and divide the number on the top by the number on the bottom. There are ways we can make this process easier, which we’ll see in the examples below.

Convert decimal to fraction – write the decimal as a fraction with 1 on the bottom. Then, keep multiplying top and bottom by 10 until the decimal becomes a whole number.

There are a number of fraction to decimal conversions that are worth memorising as this will speed up things in tests. The following are the most common ones that you can use to then convert others:

\dfrac{1}{2}=0.5

\dfrac{1}{4}=0.25

\dfrac{1}{5}=0.2

\dfrac{1}{8}=0.125

This then allows you to be able to quickly convert other fractions to decimals by multiplying, for instance

\dfrac{1}{5}=0.2 so \dfrac{2}{5}=0.4

### Fractions to Percentages

To convert between fractions and percentages we’ll use the tools we’ve already learnt to help us convert between them.

Convert percentages to fractions – a percentage is already out of 100, so we must put the value in a fraction over 100. Then, if necessary, multiply top and bottom by powers of 10 to make the values into whole numbers.

Convert fractions to percentages – firstly convert the fraction to a decimal (using the method we’ve seen), then convert that decimal to a percentage (also using the method we’ve seen).

Again you can make some fraction to percentage conversions faster by memorising the common ones below:

\dfrac{1}{2}=50%

\dfrac{1}{4}=25%

\dfrac{1}{5}=20%

\dfrac{1}{8}=12.5%

### Example 1: Percent and Decimal Conversions

a) Write 37% as a decimal.

b) Write 0.548 as a percentage.

a) To convert this to a decimal we will divide by 100, so we get

37 \div 100 = 0.37

b) To convert this to a percentage we will times by 100, so we get

0.548 \times 100 = 54.8\%

### Example 2: Fraction to Decimal

a) Write \frac{12}{25} as a decimal.

b) Write \frac{11}{8} as a decimal.

a) Dividing 12 by 25 doesn’t sound too pleasant, but there is a way we can change the fraction (before dividing top by bottom) to make life easier. Notice that 25\times 4=100 and dividing by 100 is straightforward. So, if we times top and bottom by 4 we get

\dfrac{12}{25}=\dfrac{48}{100}=0.48

So, we have successfully converted this fraction to a decimal.

b) In this case, there is no nice shortcut. We’ll just have to divide 11 by 8 in whichever way feels most comfortable – here, we’ll go for the bus stop method (make sure to put lots of zeroes after your decimal point!)

Doing this, we get the picture shown above, (Click here to revise the bus stop method) and we see that the result is

\dfrac{11}{8} = 1.375

### Example 3: Decimal to Fraction

Write 4.56 as a fraction in its simplest form.

Any number divided by 1 is equal to itself, so we can write 4.56 as \frac{4.56}{1}. Now, if we multiply top and bottom by 100 we get

\dfrac{4.56}{1}=\dfrac{4.56\times 100}{1\times 100}=\dfrac{456}{100}

All that remains now is to simplify it. Cancelling down we get.

\dfrac{456}{100} = \dfrac{228}{50} = \dfrac{114}{25}

### Example 4: Percent to Fraction

Write 48.1% as a fraction.

As mentioned, percentages are already out of 100 so

48.1\%=\dfrac{48.1}{100}

Then, multiplying top and bottom by 10 (to make the numbers whole) we get

48\% = \dfrac{481}{1000}

### Example 5: Fraction to Percent

Write \frac{4}{5} as a percentage.

Firstly, let’s convert it to a decimal. Notice that if we times top and bottom by 2, the fraction becomes

\dfrac{4}{5}=\dfrac{4\times 2}{5\times 2} = \dfrac{8}{10}

Now, dividing by 10 isn’t too tricky: 8\div 10 = 0.8. Then, to convert this decimal to a percentage, we times by 100:

0.8 \times 100 = 80\%

NOTE: Alternatively, if you can write a fraction with 100 on the denominator, then the value on the top immediately gives you what the fraction would be as a percentage. For example,

\dfrac{34}{50}=\dfrac{68}{100}=68\%

### Example Questions

1) Write 54.4% as a decimal.

We can express this percentage as a decimal simply by dividing by 100,

55.4\%\div100=0.544

2) Write 16.4% as a fraction in its simplest form.

We can express this percentage as a fraction by dividing by 100,

\dfrac{16.4}{100}

To make the numbers whole, we multiply top and bottom by 10,

\dfrac{16.4\times 10}{100 \times 10}=\dfrac{164}{1,000}

Now, we simplify until there are no common factors left. So, we find,

\dfrac{164}{1,000}=\dfrac{82}{500}=\dfrac{41}{250}

3) Write \frac{17}{40} as a decimal.

We will treat the fraction like a division and divide 17 by 40,

\;\;\;\;\;0\;0.\;\;4\;\;\;2\;\;\;5\\40\overline{\left)1{}^17.{}^{17}0{}^{10}0{}^{20}0\right.}

Therefore,

\dfrac{17}{40}=0.425

4) Write 0.256 as a fraction in its simplest form.

We can express this decimal as a fraction,

0.256=\dfrac{0.256}{1}

To make the numbers whole, we multiply top and bottom by 1000,

\dfrac{0.256}{1}\times \dfrac{1000}{1000}=\dfrac{256}{1000}

Now, we simplify until there are no common factors left. So, we find,

\dfrac{256}{1000}=\dfrac{32}{125}

5) Write \frac{13}{20} as a decimal.

A simpler method then diving 13 by 20 in its current form is to notice that 20×5=100 and dividing by 100 is straightforward. So, if we multiply top and bottom by 5 we get,

\dfrac{13}{20}\times\dfrac{5}{5}=\dfrac{65}{100} = 0.65

### Worksheets and Exam Questions

#### (NEW) Fractions to Decimals to Percentages Exam Style Questions - MME

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