Let's go through this worksheet step-by-step.

Part 1: Identifying Terminating or Repeating Decimals (Problems 1–6)

For each fraction, determine if it has a terminating or repeating decimal. A fraction has a terminating decimal if, after simplification, the only prime factors of the denominator are 2 and/or 5. If other prime factors are present, the decimal is repeating.

1. $\frac{7}{9}$: Denominator 9 has factors other than 2 or 5, so it repeats.
2. $\frac{8}{3}$: Denominator 3 also has factors other than 2 or 5, so it repeats.
3. $\frac{5}{18}$: Denominator 18 includes 3, which means it repeats.
4. $\frac{15}{8}$: Denominator 8 (factors of 2 only) means it terminates.
5. $\frac{40}{75}$: Simplify to $\frac{8}{15}$; denominator 15 includes 3, so it repeats.
6. $\frac{22}{60}$: Simplify to $\frac{11}{30}$; denominator 30 includes 3, so it repeats.

Part 2: Writing in Decimal Form (Problems 7–12)

Convert each fraction to its decimal form, using bar notation for repeating decimals where necessary.

7. $\frac{7}{9} = 0.\overline{7}$
8. $\frac{19}{15} = 1.2666\ldots = 1.2\overline{6}$
9. $\frac{43}{60} = 0.7166\ldots = 0.71\overline{6}$
10. $\frac{58}{99} = 0.\overline{58}$
11. $\frac{7}{12} = 0.5833\ldots = 0.58\overline{3}$
12. $\frac{7}{24} = 0.2916\overline{6}$

Would you like further details on any particular part or have any questions about the concepts?

Related Questions

1. What are the rules for determining if a fraction's decimal form terminates?
2. How can simplifying a fraction affect its decimal form?
3. How is bar notation used for repeating decimals?
4. What is the importance of prime factors in determining decimal types?
5. How do you convert a repeating decimal back into a fraction?

Tip

When converting fractions to decimals, divide the numerator by the denominator directly or look for known patterns to determine repeating cycles.