CAT 2025 Lesson : Percentages - Fractions to Memorise

3. Common Fractions as Decimal & Percentage

Very often, we might be given a percentage and for the purpose of calculation, we'd have to convert them to decimal or fraction. And, the reverse to convert the fraction or decimal to percentage.

Below is a common list of fractions that are expressed as percentage. A good memory of these would improve your speed in solving questions.

In the table below, we have positive fractions with different denominators. The second and third columns are the respective decimal and percentage values. The fourth column provides computational examples with the solving approach for larger fractions with the same denominator.

Fraction	Decimal	Percentage	Example
$\dfrac{1}{2}$	$0.5$	$50\%$	$\dfrac{7}{2} = 7 \times 50\% = 350\%$
$\dfrac{1}{3}$	$0.33333...$	$33.33\%$	$\dfrac{22}{3} = 7 \dfrac{1}{3} = 700\% + 33.33\% = 733.33\%$
$\dfrac{1}{4}$	$0.25$	$25\%$	$\dfrac{3}{4} = 3 \times 25\% = 75\%$
$\dfrac{1}{5}$	$0.2$	$20\%$	$\dfrac{24}{5} = 4 \dfrac{4}{5} = 400\% + 4 \times 20 \% = 480\%$
$\dfrac{1}{6}$	$0.166..$	$16.67\%$	$\dfrac{5}{6} = 1 - \dfrac{1}{6} = 100\% - 16.67\% = 83.33\%$
$\dfrac{1}{7}$	$0.1428571...$	$14.29\%$	$\dfrac{3}{7} = 3 \times 14.29\% = 42.87\%$
$\dfrac{1}{8}$	$0.125$	$12.5\%$	$\dfrac{15}{8} = 2 - \dfrac{1}{8} = 200\% - 12.5\% = 187.5\%$
$\dfrac{1}{9}$	$0.111...$	$11.11\%$	$\dfrac{7}{9} = 7 \times 11.11\% = 77.77\%$
$\dfrac{1}{10}$	$0.1$	$10\%$	$\dfrac{17}{10} = 1.7 = 170\%$
$\dfrac{1}{11}$	$0.0909...$	$9.09\%$	$\dfrac{9}{11} = 9 \times 9.09\% = 81.81\%$
$\dfrac{1}{12}$	$0.0833...$	$8.33\%$	$\dfrac{5}{12} = \dfrac{1}{2} - \dfrac{1}{12} = 50\% - 8.33\% = 41.67\%$
$\dfrac{1}{15}$	$0.0666...$	$6.67\%$	$\dfrac{4}{15} = \dfrac{1}{5} + \dfrac{1}{15} = 20\% + 6.67\% = 26.67\%$
$\dfrac{1}{16}$	$0.0625$	$6.25\%$	$\dfrac{7}{16} = \dfrac{1}{2} - \dfrac{1}{16} = 50\% - 6.25\% = 43.75\%$
$\dfrac{1}{20}$	$0.05$	$5\%$	$\dfrac{9}{20} = 9 \times 5\% = 45\%$
$\dfrac{1}{25}$	$0.04$	$4\%$	$\dfrac{17}{25} = 17 \times 4\% = 68\%$
$\dfrac{1}{30}$	$0.033...$	$3.33\%$	$\dfrac{7}{15} = \dfrac{1}{2} - \dfrac{1}{30} = 50\% - 3.33\% = 46.67\%$
$\dfrac{1}{40}$	$0.025$	$2.5\%$	$\dfrac{17}{40} = \dfrac{2}{5} + \dfrac{1}{40} = 40\% + 2.5\% = 42.5\%$
$\dfrac{1}{50}$	$0.02$	$2\%$	$\dfrac{29}{50} = 29 \times 2\% = 58\%$

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