Rational Numbers as Decimals Worksheet 1
1. Express the following rational numbers as decimals.
(i) \( \frac{9}{8} \)
Solution
\[ \begin{align*} & = \frac{9 \times 125 }{8 \times 125} \\ \\ & = \frac{1125}{1000} \\ \\ & = 1.125 \end{align*} \]
Answer \( \color{red}1.125 \)
(ii) \( \frac{615}{125} \)
Solution
\[ \begin{align*} & = \frac{615 \times 8}{125 \times 8} \\ \\ & = \frac{4920}{1000} \\ \\ & = 4.920 \end{align*} \]
Answer \( \color{red}4.920 \)
(iii) \( \frac{1}{16} \)
Solution
\[ \begin{align*} & = \frac{1 \times 625}{16 \times 625} \\ \\ & = \frac{625}{10000} \\ \\ & = 0.0625 \end{align*} \]
Answer \( \color{red}0.0625 \)
(iv) \( -\frac{3}{4} \)
Solution
\[ \begin{align*} & = -\frac{3 \times 25}{4 \times 25} \\ \\ & = -\frac{75}{100} \\ \\ & = -0.75 \end{align*} \]
Answer \( \color{red}-0.75 \)
(v) \( \frac{59}{200} \)
Solution
\[ \begin{align*} & = \frac{59 \times 5}{200 \times 5} \\ \\ & = \frac{295}{1000} \\ \\ & = 0.295 \end{align*} \]
Answer \( \color{red}0.295 \)
(vi) \( \frac{-24}{25} \)
Solution
\[ \begin{align*} & = \frac{-24 \times 4}{25 \times 4} \\ \\ & = \frac{-96}{100} \\ \\ & = -0.96 \end{align*} \]
Answer \( \color{red}-0.96 \)
(vii) \( \frac{-53}{250} \)
Solution
\[ \begin{align*} & = \frac{-53 \times 4}{250 \times 4} \\ \\ & = \frac{-212}{1000} \\ \\ & = -0.212 \end{align*} \]
Answer \( \color{red}-0.212 \)
(viii) \( \frac{47}{400} \)
Solution
\[ \begin{align*} & = \frac{47 \times 25}{400 \times 25} \\ \\ & = \frac{1175}{10000} \\ \\ & = 0.1175 \end{align*} \]
Answer \( \color{red}0.1175 \)
(ix) \( \frac{27}{800} \)
Solution
\[ \begin{align*} & = \frac{27 \times 125}{800 \times 125} \\ \\ & = \frac{3375}{100000} \\ \\ & = 0.03375 \end{align*} \]
Answer \( \color{red}0.03375 \)
(x) \( \frac{139}{625} \)
Solution
\[ \begin{align*} & = \frac{139 \times 16}{625 \times 16} \\ \\ & = \frac{2224}{10000} \\ \\ & = 0.2224 \end{align*} \]
Answer \( \color{red}0.2224 \)
(xi) \( \frac{3186}{1250} \)
Solution
\[ \begin{align*} & = \frac{3186 \times 8}{1250 \times 8} \\ \\ & = \frac{25488}{10000} \\ \\ & = 2.5488 \end{align*} \]
Answer \( \color{red}2.5488 \)
(xii) \( \frac{133}{25} \)
Solution
\[ \begin{align*} & = \frac{133 \times 4}{25 \times 4} \\ \\ & = \frac{532}{100} \\ \\ & = 5.32 \end{align*} \]
Answer \( \color{red}5.32 \)