Functional Skills: Fractions, Decimals and Percentages

Common Conversions

Fractions, decimals and percentages conversions are really useful to memorise.

These are some common fractions, decimals and percentages you should remember.

Converting Fractions to Decimals to Percentages

Fractions to Decimals:

Treat the fraction like a division, so divide the top number of the fraction by the bottom number,

e.g. $dfrac{13}{20} = 13 div 20 = 0.65$

Decimals to Percentages:

Multiply the decimal by $100$ (i.e. move the decimal point $2$ places to the right) and add a $\mathrm{\%}$ sign,

e.g. $0.65 times 100 = 65$

Note: Convert fractions to percentages by converting the fraction to a decimal and then the decimal to a percentage

e.g. $dfrac{65}{100} = 0.65 = 65$

Converting Percentages to Decimals to Fractions

Percentages to Decimals:

Divide by $100$ (i.e. move the decimal point $2$ places to the left) and remove the $\mathrm{\%}$ sign,

e.g. $65$

Decimals to Fractions:

Write the decimal as a fraction with $1$ on the bottom. Then, repeatedly multiply the top and the bottom of the fraction by $10$ until the top number turns into a whole number,

e.g. $0.65 = dfrac{0.65}{1} = dfrac{6.5}{10} = dfrac{65}{100}$

Then, you can simplify the fraction if needed: $dfrac{65}{100} = dfrac{13}{20}$

Note: To convert straight from percentages to fractions, write the percentage as a fraction with $100$ on the bottom, without the $\mathrm{\%}$ sign, and then simplify it

e.g. $65$

Comparing Fractions, Decimals and Percentages – Level 1

For Level 1, you will only need to be able to compare and order fractions, decimals and percentages, that when converted to a percentage are a multiple of $5$.

Example: Put the following in order from smallest to largest:

$25$          $dfrac{1}{5}$          $dfrac{3}{20}$          $0.3$

Step 1: Convert all of the numbers into the same form (converting all to decimals is usually the easiest):

$25$

$dfrac{1}{5} = 0.2$

$dfrac{3}{20} = 0.15$

Step 2: Rewrite the list as decimals:

$0.25$          $0.2$          $0.15$          $0.3$

Step 3: Put the list in order from smallest to largest, using the technique of ordering decimals:

$0.15$          $0.2$          $0.25$          $0.3$

Step 4: Write down the order, converting the decimals back into their original form:

$dfrac{3}{20}$          $dfrac{1}{5}$          $25$          $0.3$

Comparing Fractions, Decimals and Percentages – Level 2

You will need to be able to compare and order fractions, decimals and percentages.

Example: Put the following in order from smallest to largest:

$23$          $dfrac{1}{4}$          $dfrac{6}{25}$          $0.245$

Step 1: Convert all of the numbers into the same form (converting all to decimals is usually the easiest):

$23$

$dfrac{1}{4} = 0.25$

$dfrac{6}{25} = 0.24$

Step 2: Rewrite the list as decimals:

$0.23$          $0.25$          $0.24$          $0.245$

Step 3: Put the list in order from smallest to largest, using the technique of ordering decimals:

$0.23$          $0.24$          $0.245$          $0.25$

Step 4: Write down the order, converting the decimals back into their original form:

$23$          $dfrac{6}{25}$          $0.245$          $dfrac{1}{4}$