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In Mathematics / College | 2025-07-07

How do you write $0.\overline{1}$ as a fraction?
A. $\frac{1}{4}$
B. $\frac{1}{3}$
C. $\frac{1}{9}$
D. $\frac{1}{8}$

Asked by chikainomabrian

Answer (1)

Let x = 0. 1 .
Multiply by 10: 10 x = 1. 1 .
Subtract the equations: 9 x = 1 .
Solve for x : 9 1 ​ ​ .

Explanation

Understanding the Problem We want to express the repeating decimal 0. 1 as a fraction. The repeating decimal 0. 1 is equal to 0.11111...

Setting up the Equation Let x = 0. 1 = 0.1111...

Multiplying by 10 Multiply both sides of the equation by 10: 10 x = 1.1111...

Subtracting the Equations Subtract the first equation from the second equation: 10 x − x = 1.1111... − 0.1111...

Simplifying Simplify the equation: 9 x = 1

Solving for x Solve for x: x = 9 1 ​

Final Answer Therefore, 0. 1 = 9 1 ​ .


Examples
Repeating decimals can be used to represent fractions in a different way. For example, if you want to divide a pizza into 9 equal slices, each slice would be 0. 1 of the pizza. Understanding how to convert repeating decimals to fractions helps in real-life scenarios where precise measurements or divisions are needed.

Answered by GinnyAnswer | 2025-07-07

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