Turning a Repeating Decimal Into a Fraction Worksheet with Answer Key

What's on the worksheet

1. Write each repeating decimal as a fraction in lowest terms, showing the multiplication and subtraction:
   0.\overline{4}3.\overline{1}0.\overline{36}0.\overline{074}-0.\overline{45}
2. Convert repeating decimals that start after non-repeating digits:
   0.4\overline{2}0.3\overline{18}0.00\overline{6}2.1\overline{6}
3. Say which two multiples of x you would subtract for each decimal.
   0.\overline{5021}0.73\overline{2}0.0\overline{481}6.\overline{08}
4. Use the method in reverse: write each fraction over nines as a repeating decimal.
   \dfrac{5}{11}\dfrac{13}{33}\dfrac{4}{27}\dfrac{2}{37}
5. Word problem: the gear ratio on Mateo's bike.
6. Find the exact value of a product of two repeating decimals.
7. Explain the two-digit block pattern with the digits a and b.