FRACTIONS
TOPICS
- Expressing Fractions as Decimals
- Percentages: Percentages of Quantities; Expressing one Quantity as a Percentage of the Other; Percentage Increase and Decrease
- Ratios
- Rates and Proportions
- 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 \(10\).
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