Chapter 1: Q19. (page 10)

Write each repeating decimal as a fraction in simplest form.
$0 . \bar{5}$

Short Answer

Expert verified

The simplest form is $= \frac{5}{9}$ .

Step by step solution

Step 1. Interpret the notation.

$0 . \bar{5}$ means 0.5555…..

Step 2. Assign a variable.

Let N = 0.5555…...

Step 3. Decide by what to multiply.

Since only one-digit repeats so we multiply each side by 10.

10N = 10(0.5555…..)

10N = 5.5555…..

Step 4. Solve for N.

Subtract N from 10N, so that the repeating part eliminates.

$\frac{10 N = 5.5555 \dots . - (N = 0.5555 \dots .)}{9 N = 5}$

Then divide each side by 9 and simplify.

$\frac{9 N}{9} = \frac{5}{9}$

$N = \frac{5}{9}$

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Write each repeating decimal as a fraction in simplest form.
$0 . \bar{5}$

Short Answer

Step by step solution

Step 1. Interpret the notation.

Step 2. Assign a variable.

Step 3. Decide by what to multiply.

Step 4. Solve for N.

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Write each repeating decimal as a fraction in simplest form.0.5¯

Short Answer

Step by step solution

Step 1. Interpret the notation.

Step 2. Assign a variable.

Step 3. Decide by what to multiply.

Step 4. Solve for N.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Decision Maths

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Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

Write each repeating decimal as a fraction in simplest form.
$0 . \bar{5}$