Lesson 2: Converting Repeating Decimals to Fractions — Practice Questions

1. 1. Convert the repeating decimal $0.\overline{7}$ to a fraction in simplest form. The fraction is ___.

2. 2. Which fraction is equivalent to the repeating decimal $0.\overline{15}$?

   • A. $\frac{15}{100}$
   • B. $\frac{5}{33}$
   • C. $\frac{1}{6}$
   • D. $\frac{15}{90}$

3. 3. To convert the repeating decimal $0.\overline{456}$ to a fraction using the standard method, by which number should you multiply the equation $x = 0.\overline{456}$?

   • A. 10
   • B. 100
   • C. 1000
   • D. 10000

4. 4. When $0.\overline{123}$ is converted to a fraction and simplified, the resulting fraction is ___.

5. 5. Write the repeating decimal $0.\overline{34}$ as a fraction. The answer is ___.

6. 6. Express the repeating decimal $0.4\overline{5}$ as a fraction in simplest form. The resulting fraction is ___.

7. 7. To convert $x = 0.1\overline{7}$ to a fraction, which pair of equations should be subtracted to eliminate the repeating part?

   • A. $10x = 1.\overline{7}$ and $x = 0.1\overline{7}$
   • B. $100x = 17.\overline{7}$ and $10x = 1.\overline{7}$
   • C. $100x = 17.\overline{7}$ and $x = 0.1\overline{7}$
   • D. $1000x = 177.\overline{7}$ and $10x = 1.\overline{7}$

8. 8. Which fraction is equivalent to the repeating decimal $0.2\overline{6}$?

   • A. $\frac{26}{99}$
   • B. $\frac{8}{33}$
   • C. $\frac{4}{15}$
   • D. $\frac{2}{9}$

9. 9. When the repeating decimal $0.12\overline{3}$ is written as a fraction in simplest form, the denominator is ___.

10. 10. Let $x = 0.3\overline{1}$. When you subtract $10x$ from $100x$ to remove the repeating decimal, the result is $90x = k$. What is the value of $k$? ___