Math worksheet for practicing converting fractions to terminating and repeating decimals.

Let's solve each problem step by step. We will:

1. Divide the fraction to find its decimal form.
2. Determine if the decimal is terminating or repeating.
3. Choose the correct answer (a, b, or c) that matches the decimal and correctly shows whether it's repeating or terminating.

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1. $\frac{5}{8}$

- $5 \div 8 = 0.625$
- This is a terminating decimal (ends after 3 digits).
- So, correct choice is: c. 0.625

✔ Answer: c, Terminating

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2. $\frac{12}{40}$

- Simplify first: $\frac{12}{40} = \frac{3}{10} = 0.3$
- This is a terminating decimal.
- Option a: 0.3 → correct
- Option b: $\overline{0.3}$ → implies repeating, which is wrong
- Option c: 0.33 → incorrect value

✔ Answer: a, Terminating

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3. $\frac{11}{12}$

- $11 \div 12 = 0.91666...$ → repeats as $0.91\overline{6}$
- So, decimal is repeating
- Let's check options:
- a. 0.916 → terminates → incorrect
- b. $0.91\overline{6}$ → correct notation
- c. $0.\overline{916}$ → suggests all digits repeat → incorrect

✔ Answer: b, Repeating

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4. $\frac{4}{9}$

- $4 \div 9 = 0.444... = 0.\overline{4}$
- Repeating decimal
- Options:
- a. 0.4 → terminates → wrong
- b. $0.\overline{4}$ → correct
- c. $0.44...$ → not standard notation (missing bar)

✔ Answer: b, Repeating

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5. $\frac{33}{100}$

- $33 \div 100 = 0.33$
- This is terminating (since denominator is power of 10)
- Option a: 0.3 → too small → wrong
- Option b: $0.\overline{3}$ → repeating → wrong
- Option c: 0.33 → correct

✔ Answer: c, Terminating

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6. $\frac{1}{7}$

- $1 \div 7 = 0.142857142857... = 0.\overline{142857}$
- Repeats every 6 digits
- Option a: 0.142857 → stops → wrong
- Option b: $0.142857$ → no bar → wrong
- Option c: $0.142857$ with bar over all → correct

✔ Answer: c, Repeating

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7. $2\frac{8}{11}$

- Convert to improper fraction: $2 + \frac{8}{11} = \frac{22}{11} + \frac{8}{11} = \frac{30}{11}$
- $30 \div 11 = 2.727272... = 2.\overline{72}$
- So, it's repeating
- Options:
- a. 0.72 → wrong value
- b. 2.72 → terminates → wrong
- c. $2.\overline{72}$ → correct

✔ Answer: c, Repeating

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8. $7\frac{19}{22}$

- Convert: $7 + \frac{19}{22} = \frac{154}{22} + \frac{19}{22} = \frac{173}{22}$
- $173 \div 22 = ?$

Let’s divide:

- $22 \times 7 = 154$, remainder $19$
- $19.00 \div 22 = 0.863636...$
- So total: $7 + 0.863636... = 7.863636... = 7.8\overline{63}$

Now check options:
- a. 7.863 → terminates → wrong
- b. $7.8\overline{63}$ → correct
- c. $7.86\overline{3}$ → implies only 3 repeats → wrong

✔ Answer: b, Repeating

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9. $\frac{15}{8}$

- $15 \div 8 = 1.875$
- Terminates
- Option a: 1.875 → correct
- Option b: $1.8\overline{75}$ → repeating → wrong
- Option c: $1.\overline{875}$ → all repeat → wrong

✔ Answer: a, Terminating

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10. $\frac{55}{48}$

- $55 \div 48 = ?$

Let’s divide:

- $48 \times 1 = 48$, remainder $7$
- $7.000 \div 48 = 0.1458333...$

Wait:
- $7 \div 48 = 0.1458333...$

So:
- $55/48 = 1.1458333... = 1.1458\overline{3}$

Because after 1.1458, the 3 repeats.

Check options:
- a. 1.14583 → terminates → wrong
- b. $1.1458\overline{3}$ → correct
- c. $1.14583$ → no bar → wrong

✔ Answer: b, Repeating

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✔ Final Answers:

| # | Fraction | Decimal | Type | Correct Letter |
|---|------------------|---------------|-------------|----------------|
| 1 | $\frac{5}{8}$ | 0.625 | Terminating | c |
| 2 | $\frac{12}{40}$ | 0.3 | Terminating | a |
| 3 | $\frac{11}{12}$ | $0.91\overline{6}$ | Repeating | b |
| 4 | $\frac{4}{9}$ | $0.\overline{4}$ | Repeating | b |
| 5 | $\frac{33}{100}$| 0.33 | Terminating | c |
| 6 | $\frac{1}{7}$ | $0.\overline{142857}$ | Repeating | c |
| 7 | $2\frac{8}{11}$ | $2.\overline{72}$ | Repeating | c |
| 8 | $7\frac{19}{22}$| $7.8\overline{63}$ | Repeating | b |
| 9 | $\frac{15}{8}$ | 1.875 | Terminating | a |
|10 | $\frac{55}{48}$ | $1.1458\overline{3}$ | Repeating | b |

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✔ Fill in the blanks on the worksheet:

1. c
2. a
3. b
4. b
5. c
6. c
7. c
8. b
9. a
10. b

And for the "Tell whether the decimal is Terminating or Repeating" part:

1. Terminating
2. Terminating
3. Repeating
4. Repeating
5. Terminating
6. Repeating
7. Repeating
8. Repeating
9. Terminating
10. Repeating

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