Rational and Irrational Numbers worksheet asking students to identify which fractions result in terminating decimals.

To solve this problem, we need to determine which of the given rational numbers are terminating decimals. According to the rule provided, a rational number p/q is expressible as a terminating decimal only when the prime factors of q are 2 and 5 only.

Let's analyze each fraction step by step:

1) \(\frac{3}{8}\)
- The denominator is 8.
- Prime factors of 8: \(2 \times 2 \times 2\)
- Since the prime factors are only 2, \(\frac{3}{8}\) is a terminating decimal.

2) \(\frac{12}{35}\)
- The denominator is 35.
- Prime factors of 35: \(5 \times 7\)
- Since the prime factors include 7 (not just 2 and 5), \(\frac{12}{35}\) is not a terminating decimal.

3) \(\frac{17}{55}\)
- The denominator is 55.
- Prime factors of 55: \(5 \times 11\)
- Since the prime factors include 11 (not just 2 and 5), \(\frac{17}{55}\) is not a terminating decimal.

4) \(\frac{9}{16}\)
- The denominator is 16.
- Prime factors of 16: \(2 \times 2 \times 2 \times 2\)
- Since the prime factors are only 2, \(\frac{9}{16}\) is a terminating decimal.

5) \(\frac{5}{18}\)
- The denominator is 18.
- Prime factors of 18: \(2 \times 3 \times 3\)
- Since the prime factors include 3 (not just 2 and 5), \(\frac{5}{18}\) is not a terminating decimal.

6) \(\frac{8}{30}\)
- The denominator is 30.
- Prime factors of 30: \(2 \times 3 \times 5\)
- Since the prime factors include 3 (not just 2 and 5), \(\frac{8}{30}\) is not a terminating decimal.

7) \(\frac{45}{80}\)
- The denominator is 80.
- Prime factors of 80: \(2 \times 2 \times 2 \times 2 \times 5\)
- Since the prime factors are only 2 and 5, \(\frac{45}{80}\) is a terminating decimal.

8) \(\frac{15}{50}\)
- The denominator is 50.
- Prime factors of 50: \(2 \times 5 \times 5\)
- Since the prime factors are only 2 and 5, \(\frac{15}{50}\) is a terminating decimal.

9) \(\frac{18}{40}\)
- The denominator is 40.
- Prime factors of 40: \(2 \times 2 \times 2 \times 5\)
- Since the prime factors are only 2 and 5, \(\frac{18}{40}\) is a terminating decimal.

10) \(\frac{20}{30}\)
- The denominator is 30.
- Prime factors of 30: \(2 \times 3 \times 5\)
- Since the prime factors include 3 (not just 2 and 5), \(\frac{20}{30}\) is not a terminating decimal.

11) \(\frac{44}{60}\)
- The denominator is 60.
- Prime factors of 60: \(2 \times 2 \times 3 \times 5\)
- Since the prime factors include 3 (not just 2 and 5), \(\frac{44}{60}\) is not a terminating decimal.

12) \(\frac{10}{35}\)
- The denominator is 35.
- Prime factors of 35: \(5 \times 7\)
- Since the prime factors include 7 (not just 2 and 5), \(\frac{10}{35}\) is not a terminating decimal.

13) \(\frac{45}{160}\)
- The denominator is 160.
- Prime factors of 160: \(2 \times 2 \times 2 \times 2 \times 2 \times 5\)
- Since the prime factors are only 2 and 5, \(\frac{45}{160}\) is a terminating decimal.

14) \(\frac{35}{60}\)
- The denominator is 60.
- Prime factors of 60: \(2 \times 2 \times 3 \times 5\)
- Since the prime factors include 3 (not just 2 and 5), \(\frac{35}{60}\) is not a terminating decimal.

15) \(\frac{35}{100}\)
- The denominator is 100.
- Prime factors of 100: \(2 \times 2 \times 5 \times 5\)
- Since the prime factors are only 2 and 5, \(\frac{35}{100}\) is a terminating decimal.

16) \(\frac{8}{28}\)
- The denominator is 28.
- Prime factors of 28: \(2 \times 2 \times 7\)
- Since the prime factors include 7 (not just 2 and 5), \(\frac{8}{28}\) is not a terminating decimal.

Final Answer:
The rational numbers that are terminating decimals are: \(\frac{3}{8}\), \(\frac{9}{16}\), \(\frac{45}{80}\), \(\frac{15}{50}\), \(\frac{18}{40}\), \(\frac{45}{160}\), \(\frac{35}{100}\).