Key Idea

To convert a percentage into a fraction, write the percentage number over 100 and then simplify if possible.

Steps

1. Write the percentage as a fraction with 100 as the denominator.
2. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor.

Worked Example 1

Convert 70% into a fraction.

Solution

Step 1: Write 70% as a fraction with denominator 100:

$70\% = \frac{70}{100}$

Step 2: Simplify the fraction. Both 70 and 100 can be divided by 10:

$\frac{70 \div 10}{100 \div 10} = \frac{7}{10}$

Therefore, 70% = $\frac{7}{10}$

Worked Example 2

Convert 85% into a fraction.

Solution

$85\% = \frac{85}{100}$

Simplify by dividing both numbers by 5:

$\frac{85 \div 5}{100 \div 5} = \frac{17}{20}$

Therefore, 85% = $\frac{17}{20}$

Worked Example 3

Convert 40% into a fraction.

Solution

$40\% = \frac{40}{100}$

Simplify by dividing by 20:

$\frac{40 \div 20}{100 \div 20} = \frac{2}{5}$

Therefore, 40% = $\frac{2}{5}$

Key Idea

To convert a percentage into a decimal, first write it as a fraction with denominator 100, then divide the numerator by 100. This is the same as moving the decimal point two places to the left.

Steps

1. Write the percentage as a fraction with 100 as the denominator.
2. Divide the numerator by 100 (or simply remove the percent sign and move the decimal point two places to the left).

Worked Example 1

Convert 45% into a decimal.

Solution

Step 1: Write 45% as a fraction:

$45\% = \frac{45}{100}$

Step 2: Divide 45 by 100:

$45 \div 100 = 0.45$

Therefore, 45% = 0.45

Worked Example 2

Convert 123% into a decimal.

Solution

$123\% = \frac{123}{100} = 1.23$

Therefore, 123% = 1.23

Worked Example 3

Convert 7% into a decimal.

Solution

$7\% = \frac{7}{100} = 0.07$

Therefore, 7% = 0.07 (we need to add the zero in front to show there is no tenths place)

In Tanzania, when you go to a shop and see a discount of 25% off on a shirt that costs TSh 20,000, you can convert the percentage to a decimal to calculate the discount amount: 25% = 0.25, so the discount is 0.25 × 20,000 = TSh 5,000. This helps you know the new price quickly.