Chapter 1.2, Problem 76MR

To determine

To write: Algebraic expression for the given word phrase.

Answer to Problem 76MR

  $0.6$

Explanation of Solution

Given information:

  $0.\overline{571428}$

Calculation:

Let’s solve the given number to find decimal -

  $7\begin{array}{c}\hfill 0.5714285\\ \hfill \overline{)\begin{array}{l}40\\ -35\\ \overline{\begin{array}{l}50\\ -49\\ \overline{\begin{array}{l}10\\ -7\\ \overline{\begin{array}{l}30\\ -28\\ \overline{\begin{array}{l}20\\ -14\\ \overline{\begin{array}{l}60\\ -56\\ \overline{\begin{array}{l}40\\ -35\\ \overline{5}\\ \end{array}}\\ \end{array}}\\ \end{array}}\\ \end{array}}\end{array}}\\ \end{array}}\end{array}}\end{array}$

The quotient is a repeating decimal, in which $0.571428$ will keep on repeating, hence it can be written as $0.\overline{571428}$