Converting Fractions into Decimals

Both fractions and decimals represent quantities that may include parts of a whole. Consider a fraction of the form \(\frac{a}{b},\) where \(a\) and \(b\) are integers and \(b \neq 0\). Since fractions may also be represented as decimals, how do we convert this fraction into a decimal representing the same quantity?

If \(b\) is a power of \(10\), we are in the case for which the conversion from fraction to decimal is achieved by moving the decimal place in the numerator to the left by the power of \(10\) in the exponent of \(b\). As an example, consider the fraction \(\frac{a}{b} = \frac{8375}{1000}\). Since the denominator is \(1000 = 10^3\), the decimal conversion is achieved by moving the decimal of \(8375\) three positions to the left, giving \(8.375\). Therefore, \(\frac{8375}{1000}=8.375\).

Convert the fraction \(\frac{5}{10}\) into decimal representation.

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Since \(10 = 10^1\), we move the decimal of the numerator by \(1\) position to the left, giving

\[ \frac{5}{10} = 0.5.\]

Note that \(\frac{5}{10} = \frac{1}{2}\) and both \(\frac{1}{2} \) and \(0.5\) represent one half of a whole. \(_\square\)

Convert the fraction \(\frac{19}{100}\) into decimal representation.

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Since \(100 = 10^2\), we move the decimal of the numerator by \(2\) positions to the left, giving

\[ \frac{19}{10} = 0.19.\ _\square\]

Convert the fraction \(\frac{47}{10000}\) into decimal representation.

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Since \(10000 = 10^4\), we move the decimal of the numerator by \(4\) positions to the left, giving

\[ \frac{47}{10000} = 0.0047.\ _\square\]

Convert the fraction \(2\frac{7}{100}\) into decimal representation.

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Since \(2 \frac{7}{100} = \frac{207}{100}\) and \(100 = 10^2\), we move the decimal of the numerator by \(2\) positions to the left, which gives

\[ \frac{207}{100} = 2.07.\ _\square\]