FRACTIONS

TOPICS

1. Expressing Fractions as Decimals
2. Percentages: Percentages of Quantities; Expressing one Quantity as a Percentage of the Other; Percentage Increase and Decrease
3. Ratios
4. Rates and Proportions
5. Word Problems Involving Fractions

Expressing Fractions as Decimals

There are two methods of doing this conversion. There is a general method that can be used at any time and on any type of vulgar fraction. There is also another method where the denominator of the fraction contains power/powers of ten.

In this second case, the given fraction can first be converted to an equivalent fraction.

Examples:

Convert the following common fractions to decimal fractions (decimal numbers).

\(\frac{2}{5}, \frac{3}{4}, \frac{144}{225}\)

Solutions:

First: We can use the equivalent fractions method, before the general method.

◊ Write \(\frac{2}{5}\) as \(\frac{2}{5}\)

\(= \frac{2 × 2}{5 × 2} = \frac{4}{10} = 0.4\)

\(∴ \frac{2}{5} = 0.4\)

◊ Write \(\frac{3}{4}\) as \(\frac{3}{4}\)

\(= \frac{3 × 25}{4 × 25} = \frac{75}{100} = 0.75\)

\(∴ \frac{3}{4} = 0.75\)

◊ Write \(\frac{44}{125}\) as \(\frac{44}{125}\)

\(= \frac{44 × 8}{125 × 8} = \frac{352}{1000} = 0.352\)

\(∴ \frac{44}{125} = 0.352\)

Second: The general method (for all conditions) is used when the denominator of the given fraction does not contain power(s) of \(10\).