Terminating and Repeating Decimals worksheet - Free Printable

To solve the problem, we need to convert each fraction into its decimal form and determine whether the resulting decimal is terminating or repeating. Then, we will choose the correct way to write the decimal based on the options provided.

Terminating vs. Repeating Decimals:

- Terminating decimals end after a finite number of digits.
- Repeating decimals have one or more digits that repeat indefinitely.

Step-by-Step Solution:

#### 1. \( \frac{5}{8} \)
- Perform the division: \( 5 \div 8 = 0.625 \)
- The decimal terminates after three digits.
- Correct answer: c. 0.625

#### 2. \( \frac{12}{40} \)
- Simplify the fraction: \( \frac{12}{40} = \frac{3}{10} \)
- Perform the division: \( 3 \div 10 = 0.3 \)
- The decimal terminates after one digit.
- Correct answer: a. 0.3

#### 3. \( \frac{11}{12} \)
- Perform the division: \( 11 \div 12 = 0.91666\ldots \) (repeating 6)
- The decimal repeats.
- Correct answer: b. 0.91\(\overline{6}\)

#### 4. \( \frac{4}{9} \)
- Perform the division: \( 4 \div 9 = 0.4444\ldots \) (repeating 4)
- The decimal repeats.
- Correct answer: b. 0.\(\overline{4}\)

#### 5. \( \frac{33}{100} \)
- Perform the division: \( 33 \div 100 = 0.33 \)
- The decimal terminates after two digits.
- Correct answer: c. 0.33

#### 6. \( \frac{1}{7} \)
- Perform the division: \( 1 \div 7 = 0.142857142857\ldots \) (repeating 142857)
- The decimal repeats.
- Correct answer: c. 0.\(\overline{142857}\)

#### 7. \( 2 \frac{8}{11} \)
- Convert the mixed number to an improper fraction: \( 2 \frac{8}{11} = \frac{2 \times 11 + 8}{11} = \frac{30}{11} \)
- Perform the division: \( 30 \div 11 = 2.727272\ldots \) (repeating 72)
- The decimal repeats.
- Correct answer: c. 2.\(\overline{72}\)

#### 8. \( 7 \frac{19}{22} \)
- Convert the mixed number to an improper fraction: \( 7 \frac{19}{22} = \frac{7 \times 22 + 19}{22} = \frac{173}{22} \)
- Perform the division: \( 173 \div 22 = 7.8636363\ldots \) (repeating 63)
- The decimal repeats.
- Correct answer: c. 7.8\(\overline{63}\)

#### 9. \( \frac{15}{8} \)
- Perform the division: \( 15 \div 8 = 1.875 \)
- The decimal terminates after three digits.
- Correct answer: a. 1.875

#### 10. \( \frac{55}{48} \)
- Perform the division: \( 55 \div 48 = 1.1458333\ldots \) (repeating 3)
- The decimal repeats.
- Correct answer: c. 1.1458\(\overline{3}\)

Final Answers:

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

Boxed Answer:

\[
\boxed{
\begin{array}{ll}
1. & \text{c} \\
2. & \text{a} \\
3. & \text{b} \\
4. & \text{b} \\
5. & \text{c} \\
6. & \text{c} \\
7. & \text{c} \\
8. & \text{c} \\
9. & \text{a} \\
10. & \text{c} \\
\end{array}
}
\]