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3. Representation in the form of a decimal fraction

Conversion of ordinary and mixed fraction into a decimal fraction:

To represent ordinary fractions

\frac{1}{5}; \frac{3}{4}; \frac{2}{125}

in the form of decimal fractions, they are first expanded by a number so that the denominator produces a unit digit (\(10, 100, 1000\), etc.)

Expanding the first fraction by \(2\), the second by \(25\), and the third by \(8\), we get:

\begin{array}{l} \frac{1^{(\times 2)}}{5} = \frac{2}{10} = 0.2 \\ \frac{3^{(\times 25)}}{4} = \frac{75}{100} = 0.75 \\ \frac{2^{(\times 8)}}{125} = \frac{16}{1000} = 0.016 \end{array}

Important!

Not all ordinary fractions can be converted to decimal.

Example:

Fractions

\frac{1}{3}; \frac{2}{7}; \frac{5}{19}

cannot be expanded as the denominator numbers are not the decimals of 10, 100, 1000, etc. Such fractions will produce recurring decimals.

Similar to ordinary fraction, the mixed fraction is also converted.

Here the fractional part is expanded to obtain the denominator with a unit digit (\(10, 100, 1000\), etc.)

The whole number is written before the point, and the fractional part is written after the point.

\begin{array}{l} 73 \frac{1^{(\times 5)}}{2} = 73 \frac{5}{10} = 73.5 \\ 102 \frac{17^{(\times 2)}}{50} = 102 \frac{34}{100} = 102.34 \\ 9 \frac{11^{(\times 4)}}{250} = 9 \frac{44}{1000} = 9.044 \end{array}

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