Chapter 3, Problem 22CR

To determine

To write: the provided decimals in fraction in their simplest form.

Answer to Problem 22CR

The simplest form $10.\overline{27}$ is $10\frac{3}{11}$

Explanation of Solution

Given information: the decimal number provided in the question,

  $10.\overline{27}$

Calculation:

Let,

  $n=\mathrm{10.2727....}$

Multiply both sides with 100

  $\begin{array}{l}100n=100\left(\mathrm{10.2727...}\right)\\ 100n=\mathrm{1027.2727...}\end{array}$

Subtract n from 100n ,

  $\begin{array}{l}100n-n=\mathrm{1027.2727...}-\mathrm{10.2727...}\\ 99n=1017\\ n=\frac{1017}{99}\\ n=10\frac{3}{11}\end{array}$

Hence, the simplest form of $10.\overline{27}$ is $10\frac{3}{11}$ .