Conversion from Percentage to Decimal and Decimal to Fraction – JSS1 Mathematics Lesson Note (First Term)

A fraction can be changed to a decimal by dividing the numerator by the denominator. A decimal can be changed to a fraction by writing its digits over 10, 100 or 1000 and simplifying. A percentage is a fraction with 100 as its denominator, so it is changed to a fraction by dividing by 100.

Behavioural objectives

By the end of the lesson, students should be able to:

• change a fraction into a terminating decimal;
• change a decimal into a fraction in its lowest terms;
• express a percentage, including one with a mixed number, as a fraction in its simplest form.

How do we convert a fraction to a decimal?

To convert a fraction into a decimal, first rewrite the numerator as a decimal, then divide it by the denominator.

Example 1

(a) Change 3/4 into a terminating decimal number. (b) Change 5/8 to a decimal fraction.

Solution

(a) The numerator 3 can be written as a decimal number as 3.0, 3.00 or 3.000.

4 divides 3 zero times, then add zero. 4 goes into 30 seven times and it remains 2. Add 0 to make it 20, and 4 in 20 gives 5.

Therefore, 3/4 = 0.75.

(b) 8 divides 5 zero times, then add zero to make it 50. 8 in 50 gives 6 and it remains 2. Add zero to make it 20. 8 in 20 is 2 and it remains 4. Add zero to give 40, and 8 in 40 is 5.

Therefore, 5/8 = 0.625.

How do we convert a decimal to a fraction?

To change a decimal into a fraction, count the digits after the decimal point. Write the digits as the numerator over the appropriate power of 10, that is 10, 100 or 1000. Then simplify.

Example 2

Convert each of the following decimal numbers into a fraction in the lowest terms: (a) 0.067 (b) 0.64

Solution

(a) 0.067 = 67/1000 (3 digits after the decimal point, so the denominator is 1000).

(b) 0.64 = 64/100 (2 digits after the decimal point, so the denominator is 100). Divide the numerator and the denominator by 4 to get 16/25.

How do we convert a percentage to a fraction?

A percentage is a special type of fraction with 100 as the denominator. Therefore, to change a percentage to a fraction, divide by 100 and simplify.

Example 3

Express each of the following as a fraction in its simplest form: (a) 30% (b) 45% (c) 16½%

Solution

(a) 30% = 30/100. The zeros cancel each other. The answer is 3/10.

(b) 45% = 45/100. Divide both numerator and denominator by 5 to get 9/20.

(c) 16½% = 33/2 × 1/100. Change the mixed number to an improper fraction, then multiply it by 1/100. The answer is 33/200.

Evaluation

1. Explain how to change a fraction into a decimal.
2. What do you count when changing a decimal into a fraction?
3. Change 0.75 into a fraction in its lowest terms.
4. Express 60% as a fraction in its simplest form.

Assignment

1. Convert 0.125 into a fraction in its lowest terms.
2. Express 25% as a fraction in its simplest form.
3. Express 12% as a fraction in its simplest form.