Question

Express the following in decimal form.

$\frac{7}{5}, \frac{3}{4}, \frac{23}{10}, \frac{5}{3}, \frac{17}{6}, \frac{22}{7}$

Accepted Answer

Given: $\frac{7}{5}, \frac{3}{4}, \frac{23}{10}, \frac{5}{3}, \frac{17}{6}, \frac{22}{7}$ and $\frac{22}{7}$

Now, $\frac{7}{5}$

$\begin{matrix} 1 & . & 4 \\ 5 & 7 \\ - & 5 \\ 2 & 0 \\ - & 2 & 0 \\ 0 \end{matrix}$

So, $\frac{7}{5} = 1.4$

$\begin{matrix} 0 & . & 7 & 5 \\ 4 & 3 & 0 \\ - & 2 & 8 \\ 2 & 0 \\ - & 2 & 0 \\ 0 \end{matrix}$

So, $\frac{3}{4} = 0.75$

Now, $\frac{23}{10} = 2.3$

$\begin{matrix} 1 & . & 6 & 6 & 6 \\ 3 & 5 \\ - & 3 \\ 2 & 0 \\ - & 1 & 8 \\ 2 & 0 \\ - & 1 & 8 \\ 2 & 0 \\ - & 1 & 8 \\ 2 \end{matrix}$

Therefore, $\frac{5}{3} = 1.666 . . . .$ $= 1 . \bar{6}$

$\begin{matrix} 2 & . & 8 & 3 & 3 \\ 6 & 1 & 7 \\ - & 1 & 2 \\ 5 & 0 \\ - & 4 & 8 \\ 2 & 0 \\ - & 1 & 8 \\ 2 & 0 \\ - & 1 & 8 \\ 2 \end{matrix}$

Therefore, $\frac{17}{6} = 2.8333 . . . .$ $= 2.8 \bar{3}$

$\begin{matrix} 3 & . & 1 & 4 & 2 & 8 & 5 & 7 & 1 & 4 \\ 7 & 2 & 2 \\ 2 & 1 \\ 1 & 0 \\ - & 7 \\ 3 & 0 \\ - & 2 & 8 \\ 2 & 0 \\ - & 1 & 4 \\ 6 & 0 \\ - & 5 & 6 \\ 4 & 0 \\ - & 3 & 5 \\ 5 & 0 \\ - & 4 & 9 \\ 1 & 0 \\ - & 7 \\ 3 & 0 \\ - & 2 & 8 \\ 2 \end{matrix}$

Therefore, $\frac{22}{7} = 3.14285714 . . . .$ $= 3 . \bar{14285714}$

Hence, $\frac{7}{5} = 1.4, \frac{3}{4} = 0.75, \frac{23}{10} = 2.3, \frac{5}{3} = 1 . \bar{6}, \frac{17}{6} = 2.8 \bar{3}$ and $\frac{22}{7} = 3 . \bar{14285714}$

Telangana Board Solutions for Chapter: Rational Numbers, Exercise 13: Exercise 13

Telangana Board Mathematics Solutions for Exercise - Telangana Board Solutions for Chapter: Rational Numbers, Exercise 13: Exercise 13

Questions from Telangana Board Solutions for Chapter: Rational Numbers, Exercise 13: Exercise 13 with Hints & Solutions

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