Chapter 11.2, Problem 42WE

a.

To determine

To express the given fractions as repeating decimals.

Answer to Problem 42WE

  $\frac{1}{7}=0.\overline{142857}$ , $\frac{6}{7}=0.\overline{857142}$

Explanation of Solution

Given:

The given fractions are-

  $\frac{1}{7}$ and $\frac{6}{7}$

Calculation:

The given fraction $\frac{1}{7}$ can be written as

  $\begin{array}{l}\frac{1}{7}=0.14285714285\\ \frac{1}{7}=0.\overline{142857}\end{array}$

Similarly, the given fraction $\frac{6}{7}$ can be written as

  $\begin{array}{l}\frac{6}{7}=0.85714285714\\ \frac{6}{7}=0.\overline{857142}\end{array}$

b.

To determine

To find the relationship between the block of digits that repeat in part (a).

Answer to Problem 42WE

  $6$ times.

Explanation of Solution

Given:

The given fractions are-

  $\frac{1}{7}$ and $\frac{6}{7}$

Calculation:

The second block of the fraction that repeat is six times the first block.

c.

To determine

To express the given fractions as decimals.

Explanation of Solution

Given:

The given fractions are-

  $\frac{3}{7},\frac{4}{7}$ and $\frac{5}{7}$

Calculation:

The given fraction $\frac{3}{7}$ can be written as

  $\frac{3}{7}=0.42857142857$

Similarly, the given fraction $\frac{4}{7}$ can be written as

  $\frac{4}{7}=0.57142857142$

Similarly, the given fraction $\frac{5}{7}$ can be written as

  $\frac{5}{7}=0.71428571428$