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

$$\frac{207}{100} = 2.07.\ _\square$$