So how do you convert percentages to fractions and decimals and vice versa? This post will show examples of each.

**Convert a percentage to a fraction**:

This one is easy as if you remember, a percentage is already a fraction where the numerator is displayed and the denominator is 100. So you just create the fraction and simplify it (see my posts on fractions):

\[{40}{\%}\hspace{0.33em}{=}\hspace{0.33em}\frac{40}{100}\hspace{0.33em}{=}\hspace{0.33em}\frac{{2}{0}\hspace{0.33em}\times\hspace{0.33em}{2}}{{20}\hspace{0.33em}\times\hspace{0.33em}{5}\hspace{0.33em}}\hspace{0.33em}{=}\hspace{0.33em}\frac{2}{5}

\]

2. **Convert a percentage to a decimal**:

This one is just a matter of moving the decimal point, two places to the left. Keep in mind that the decimal point will not usually show at the end of integer percentage, but you can assume it to be at the end of the number:

37% = 37.% = 0.37

18.5% = 0.185

112% = 1.12

0.15% = 0.0015

Any 0’s at the end of the decimal, can be left off:

40% = 0.40 = 0.4

**3. Convert a decimal to a percentage:**

This is just the opposite of of the above: you just move the decimal point two places to the right, then add the % symbol:

0.25 = 25% (if an integer results, you can leave the decimal point off)

0.2786 = 27.86%

0.002 = 0.2%

2.345 = 234.5%

**4. Convert a fraction to a percentage:**

Here you multiply by 100/1, simplify, then multiply numerators together and denominator together. It is advisable to simplify before multiplying:

\[\frac{3}{5}\hspace{0.33em}\times\hspace{0.33em}\frac{100}{1}\hspace{0.33em}{=}\hspace{0.33em}\frac{3}{\rlap{/}{5}\hspace{0.33em}\times\hspace{0.33em}{1}}\hspace{0.33em}\times\hspace{0.33em}\frac{\rlap{/}{5}\hspace{0.33em}\times\hspace{0.33em}{20}}{1}\hspace{0.33em}{=}\hspace{0.33em}{60}{\%}

\]

Sometimes though, not as much cancels and you will need to do some division in the end (long or short – see my post on long division):

\[\frac{8}{9}\hspace{0.33em}\times\hspace{0.33em}\frac{100}{1}\hspace{0.33em}{=}\hspace{0.33em}\frac{800}{9}\hspace{0.33em}{=}\hspace{0.33em}{800}\hspace{0.33em}\div\hspace{0.33em}{9}\hspace{0.33em}{=}\hspace{0.33em}{88}{.}{89}{\%}

\]

In my next post, I will show how to do some of the more common problems using percentages.