Chapter 1: Q3P (page 1)

Use equation (1.8) to find the fractions that are equivalent to the following repeating decimals:
$0.55555 . . .$

Short Answer

Expert verified

The equivalent fraction for $0.55555 . . .$ is $\frac{5}{9}$ .

Step by step solution

Explanation of solution

Given number is $0.55555 . . .$ .

The expression for sum of infinite GP series is $S = \frac{a}{1 - r}$ .

Where, S is the sum of GP up to infinite terms.

Equivalent fraction

Fractions having the same numerator and denominator but different numerators and denominators are called equivalent fractions.

Calculation

An example of how to write the number is as follows:

$0.55555 . . . = 0.5 + 0.05 + 0.005 + 0.0005 + . . . . + 0.5 {(\frac{1}{10})}^{n}$

The words will create GP with $a = 0.5$ and $r = 1 / 10$ .

Substitute 0.5 for a and 1/10 for r in above equation.

$\begin{array}{rcl} S & = & \frac{0.5}{1 - \frac{1}{10}} \\ = & \frac{\frac{5}{10}}{\frac{9}{10}} \\ = & \frac{5}{9} \end{array}$

Hence, the fraction is $\frac{5}{9}$ .

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Use equation (1.8) to find the fractions that are equivalent to the following repeating decimals:
$0.55555 . . .$

Short Answer

Step by step solution

Explanation of solution

Equivalent fraction

Calculation

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Use equation (1.8) to find the fractions that are equivalent to the following repeating decimals:0.55555...

Short Answer

Step by step solution

Explanation of solution

Equivalent fraction

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Linear Momentum

Scientific Method Physics

Nuclear Physics

Thermodynamics

Classical Mechanics

Study anywhere. Anytime. Across all devices.

Use equation (1.8) to find the fractions that are equivalent to the following repeating decimals:
$0.55555 . . .$