Equivalent fractions, decimals and percentages
In a nutshell
Fractions, decimals and percentages are all ways of representing quantities with parts that are less than one. Learning to convert between them is an important skill used all the time in maths.
Equivalence
Definition
Equivalent means equal in value. If any fractions, decimals or percentages are equivalent to one another, they represent the same value.
Equivalent simple fractions, decimals and percentages
There are some simple fractions that it's really useful to know the decimal and percentage equivalences for.
FRACTION
 DECIMAL
 PERCENTAGE  VISUAL REPRESENTATION

$0$
 $0$
 $0\%$
 
$\dfrac{1}{4}$
 $0.25$
 $25\%$
 
$\dfrac{1}{2}$
 $0.5$
 $50\%$
 
$\dfrac{3}{4}$
 $0.75$
 $75\%$
 
$1$
 $1$
 $100\%$
 
Converting between other fractions, decimals and percentages
For the more complicated fractions, decimals and percentages, there are steps you can use to convert between the different forms.
Fractions to decimals to percentages
PROCEDURE
1.
 Starting with a fraction, divide the numerator by the denominator to get a decimal. 
2.
 Multiply the decimal by one hundred to get a percentage.

Note: To turn trickier fractions into decimals, you might need to use a calculator or use the bus stop method!
Percentages to fractions to decimals
procedure
1.
 Write the percentage as a the number out of one hundred to get a fraction. (Simplify if required). 
2.
 Divide the numerator by the denominator to get a decimal. 
Tip: Percent means 'out of one hundred'.
Example 1
What is $67\%$ as a fraction and decimal?
Write $67\%$ as a fraction with $100$ as the denominator.
$67\%=\underline{\dfrac{67}{100}}$
Divide $67$ by $100$ to get a decimal.
$67\div100=\underline{0.67}$
Example 2
What is $\dfrac{3}{8}$ as a decimal and percentage?
Divide $3$ by $8$ to get a decimal.
$8\overset{\,\,\,\,\,0\,.\,\,\,\,3\,\,\,\,\,7\,\,\,5\,\,}{\overline{\smash{)}\cancel3.^30^60^40}} \\$
$3\div8=\underline{0.375}$
Multiply by one hundred to get a percentage.
$0.375\times100=\underline{37.5\%}$