Write 12.5% as a fraction in its simplest form.

Class 7Comparing QuantitiesComparing Quantities

A $\frac{1}{80}$
B $\frac{5}{4}$
C $\frac{1}{8}$
D $\frac{125}{100}$

Step-by-Step Solution

Per cent means "out of 100", so 12.5% =

\frac{12.5}{100}

. Clear the decimal by multiplying top and bottom by 10:

\frac{125}{1000}

. Divide both by 125:

\frac{1}{8}

. The trap in

\frac{125}{100}

and

\frac{5}{4}

is dropping the decimal point and reading the number as 125%.

\frac{1}{80}

comes from dividing by 1000 instead of 100.

Answer: C)

\frac{1}{8}

Key idea: Three forms of the same number

Fractions, decimals, and percentages are three notations for the same idea. Convert freely:

- **Fraction → percentage**: multiply by 100.

\frac{3}{5} = \frac{3}{5} \times 100% = 60%

.
- **Percentage → fraction**: divide by 100 and simplify.

75% = \frac{75}{100} = \frac{3}{4}

.
- **Decimal → percentage**: shift two places right. 0.34 = 34%.
- **Percentage → decimal**: shift two places left. 8% = 0.08.

With practice, this becomes automatic and you can move between forms without thinking.

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