Chapter 1: Q22. (page 10)

Write each repeating decimal as a fraction in simplest form.
$0 . \bar{21}$

Short Answer

Expert verified

The simplest form is $= \frac{21}{99}$

Step by step solution

Step 1. Interpret the notation.

$0 . \bar{21}$ means 0.212121…..

Step 2. Assign a variable.

Let N = 0. 212121…...

Step 3. Decide by what to multiply.

Since two-digits repeat so we multiply each side by 100.

100N = 100(0.212121…..)

100N = 21.212121…..

Step 4. Solve for N.

Subtract N from 100N, so that the repeating part eliminates.

$100 N = 21.212121 \dots . \frac{- (N = 0.212121 \dots .)}{99 N = 21}$

Then divide each side by 99 and simplify.

$\frac{99 N}{99} = \frac{21}{99}$

$N = \frac{21}{99}$

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Write each repeating decimal as a fraction in simplest form.
$0 . \bar{21}$

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.0.21¯

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

Calculus

Geometry

Applied Mathematics

Discrete Mathematics

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Write each repeating decimal as a fraction in simplest form.
$0 . \bar{21}$