How do you write 0.{1} as a fraction? Choices: (A)1/9 (B)1/8 (C)1/3 (D)1/4

Recognize decimal pattern: Recognize the repeating decimal. 0.{1} means 0.1111... Shift decimal point: Let x = 0.1111... Multiply both sides by 10 to shift the decimal point. 10x = 1.1111... Subtract and simplify: Subtract the original x from 10x. 10x - x = 1.1111... - 0.1111... This gives 9x = 1 Solve for x: Solve for x by dividing both sides by 9. x = 1/9

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Grade 8

Convert between repeating decimals and fractions

Full solution

Q. How do you write

0.\overline{1}

as a fraction?

\newline

Choices:

\newline

(A)

\frac{1}{9}

\newline

(B)

\frac{1}{8}

\newline

(C)

\frac{1}{3}

\newline

(D)

\frac{1}{4}

Recognize decimal pattern: Recognize the repeating decimal. 0.ar{1} means $0.1111...$
Shift decimal point: Let $x = 0.1111\ldots$ Multiply both sides by $10$ to shift the decimal point. $10x = 1.1111\ldots$
Subtract and simplify: Subtract the original $x$ from $10x$ . $10x - x = 1.1111... - 0.1111...$ This gives $9x = 1$
Solve for x: Solve for x by dividing both sides by $9$ . $x = \frac{1}{9}$