Chapter 3, Problem 31SGR

To determine

To calculate:To convert decimal into a fraction or mixed number in simplest form

Answer to Problem 31SGR

Decimalcan be represented in mixed fraction as $10\frac{37}{99}$

Explanation of Solution

Given information:Decimal is $10.\overline{2}\overline{7}$

Calculation:

Decimal is given as

  $10.\overline{2}\overline{7}$

Here, decimal is a repeating decimal

Let us assume

  $x=10.272727$ ------(1)

Here, repeating digit is 27, thus, to place the repeating digit to the left of decimal point, decimal point needs to be moved 2place to the right

Multiplying the (1) by 100,

  $100x=1027.272727$ -----(2)

Subtracting (1) from (2),

  $99x=1027$

Thus, on solving above

  $\begin{array}{l}x=\frac{1027}{99}\\ x=10\frac{37}{99}\end{array}$

Hence, decimalcan be represented in mixed fraction as $10\frac{37}{99}$