Understanding Percentages, Decimals, and Fractions

What is a Percentage?

When we say "Percent", we mean "per 100".

One percent (1%) means 1 per 100.

Decimals, Fractions, and Percentages

Decimals, fractions, and percentages are just different ways of showing the same value. For example:

• A half can be written as:
  • Fraction: $\frac{1}{2}$
  • Decimal: $0.5$
  • Percentage: $50\%$

Example:

Find 8% of 50.

8% of 50 is the same as 50% of 8.

50% of 8 is 4.

So, 8% of 50 is 4.

Common Fractions with Decimal and Percent Equivalents

Fraction	Decimal	Percentage
$\frac{1}{2}$	$0.5$	$50\%$
$\frac{1}{3}$	$0.333\dots$	$33.333\dots \%$
$\frac{2}{3}$	$0.666\dots$	$66.666\dots \%$
$\frac{1}{4}$	$0.25$	$25\%$
$\frac{3}{4}$	$0.75$	$75\%$
$\frac{1}{5}$	$0.2$	$20\%$
$\frac{2}{5}$	$0.4$	$40\%$
$\frac{3}{5}$	$0.6$	$60\%$
$\frac{4}{5}$	$0.8$	$80\%$
$\frac{1}{6}$	$0.1666\dots$	$16.666\dots \%$
$\frac{5}{6}$	$0.8333\dots$	$83.333\dots \%$
$\frac{1}{8}$	$0.125$	$12.50\%$
$\frac{3}{8}$	$0.375$	$37.50\%$
$\frac{5}{8}$	$0.625$	$62.50\%$
$\frac{7}{8}$	$0.875$	$87.50\%$
$\frac{1}{9}$	$0.111\dots$	$11.111\dots \%$
$\frac{2}{9}$	$0.222\dots$	$22.222\dots \%$
$\frac{4}{9}$	$0.444\dots$	$44.444\dots \%$
$\frac{5}{9}$	$0.555\dots$	$55.555\dots \%$
$\frac{7}{9}$	$0.777\dots$	$77.777\dots \%$
$\frac{8}{9}$	$0.888\dots$	$88.888\dots \%$
$\frac{1}{10}$	$0.1$	$10\%$
$\frac{1}{12}$	$0.08333\dots$	$8.333\dots \%$
$\frac{1}{16}$	$0.0625$	$6.25\%$
$\frac{1}{32}$	$0.03125$	$3.13\%$

Conversion Methods

A. From Percent to Decimal

To convert a percentage to a decimal:

1. Divide by 100.
2. Remove the "%" sign.

B. From Decimal to Percent

To convert a decimal to a percentage:

1. Multiply by 100.
2. Add the "%" sign.

C. From Fraction to Decimal

To convert a fraction to a decimal:

1. Divide the numerator (top number) by the denominator (bottom number).

D. From Decimal to Fraction

To convert a decimal to a fraction:

1. Remove the decimal by adding the denominator with the appropriate number of zeros.
2. Simplify the fraction.

E. From Fraction to Percentage

To convert a fraction to a percentage:

1. Multiply the fraction by 100.
2. Reduce it to decimal form and add the "%" sign.

F. From Percentage to Fraction

To convert a percentage to a fraction:

1. First, convert the percentage to a decimal (divide by 100).
2. Then, use the steps for converting a decimal to a fraction.

Important Formulas

• $x\%\text{of}y=y\%\text{of}x=\frac{x\times y}{100}$
• To convert $\%$ to decimal: Divide by 100.
• To convert decimal to $\%$: Multiply by 100.
• To convert fraction to decimal: Divide numerator by denominator.
• To convert decimal to fraction: Write decimal as a fraction and simplify.

Practice Questions

1. Convert 45% to a decimal.
2. Convert 0.75 to a percentage.
3. Convert $\frac{3}{8}$ to a decimal.
4. Convert 0.6 to a fraction.
5. Convert $\frac{5}{6}$ to a percentage.
6. Convert 12.5% to a fraction.