Chapter 11.2, Problem 26WE

To determine

To find: The fractional form of the given rational number

Answer to Problem 26WE

The rational number in the fractional form is $-\frac{135}{99}$

Explanation of Solution

Given information:

The given rational number is:

  $N=-1.\overline{36}$...........(1)

Since there are 2 digits in the repeating block, multiply the rational number by 100.

  $\begin{array}{l}100N=1.\overline{36}\times 100\\ 100N=136.\overline{36}\end{array}$ ...........(2)

Add Equation (1) from (2):

  $\begin{array}{l}100N-N=136.\overline{36}-1.\overline{36}\\ 99N=135\\ N=-\frac{135}{99}\end{array}$

Thus, the rational number in the fractional form is $-\frac{135}{99}$