How do you write 0.{09} as a fraction? Choices: (A)1/9 (B)1/5 (C)1/11 (D)1/12

Recognize repeating decimal: Step 1: Recognize the repeating decimal. 0.{09} means 0.090909... Shift decimal point: Step 2: Let x = 0.090909... Multiply x by 100 to shift the decimal point two places to the right. 100x = 9.090909... Subtract and simplify: Step 3: Subtract the original x from 100x. 100x - x = 9.090909... - 0.090909... This gives 99x = 9 Solve for x: Step 4: Solve for x by dividing both sides by 99. x = 9 / 99 Final fraction: Step 5: Simplify the fraction 9/99. Divide numerator and denominator by 9. x = 1 / 11

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How do you write $0.\overline{09}$ as a fraction? $\newline$ Choices: $\newline$ (A) $\frac{1}{9}$ $\newline$ (B) $\frac{1}{5}$ $\newline$ (C) $\frac{1}{11}$ $\newline$ (D) $\frac{1}{12}$

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{09}

as a fraction?

\newline

Choices:

\newline

(A)

\frac{1}{9}

\newline

(B)

\frac{1}{5}

\newline

(C)

\frac{1}{11}

\newline

(D)

\frac{1}{12}

Recognize repeating decimal: Step $1$ : Recognize the repeating decimal. $0.\overline{09}$ means $0.090909\ldots$
Shift decimal point: Step $2$ : Let $x = 0.090909...$ Multiply $x$ by $100$ to shift the decimal point two places to the right. $100x = 9.090909...$
Subtract and simplify: Step $3$ : Subtract the original $x$ from $100x$ . $100x - x = 9.090909... - 0.090909...$ This gives $99x = 9$
Solve for x: Step $4$ : Solve for x by dividing both sides by $99$ . $x = \frac{9}{99}$
Final fraction: Step $5$ : Simplify the fraction $\frac{9}{99}$ . Divide numerator and denominator by $9$ . $x = \frac{1}{11}$