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 \( \frac{p}{q} \) is expressible as a terminating decimal only when the prime factors of \( q \) are 2 and 5 only.
Let's go through each fraction step by step:
1. \( \frac{3}{8} \):
- Prime factors of 8: \( 2^3 \)
- Only prime factor is 2.
-
Terminating
2. \( \frac{12}{35} \):
- Prime factors of 35: \( 5 \times 7 \)
- Contains prime factor 7.
-
Non-terminating
3. \( \frac{17}{55} \):
- Prime factors of 55: \( 5 \times 11 \)
- Contains prime factor 11.
-
Non-terminating
4. \( \frac{9}{16} \):
- Prime factors of 16: \( 2^4 \)
- Only prime factor is 2.
-
Terminating
5. \( \frac{5}{18} \):
- Prime factors of 18: \( 2 \times 3^2 \)
- Contains prime factor 3.
-
Non-terminating
6. \( \frac{8}{30} \):
- Simplify \( \frac{8}{30} = \frac{4}{15} \)
- Prime factors of 15: \( 3 \times 5 \)
- Contains prime factor 3.
-
Non-terminating
7. \( \frac{45}{80} \):
- Simplify \( \frac{45}{80} = \frac{9}{16} \)
- Prime factors of 16: \( 2^4 \)
- Only prime factor is 2.
-
Terminating
8. \( \frac{15}{50} \):
- Simplify \( \frac{15}{50} = \frac{3}{10} \)
- Prime factors of 10: \( 2 \times 5 \)
- Only prime factors are 2 and 5.
-
Terminating
9. \( \frac{18}{40} \):
- Simplify \( \frac{18}{40} = \frac{9}{20} \)
- Prime factors of 20: \( 2^2 \times 5 \)
- Only prime factors are 2 and 5.
-
Terminating
10. \( \frac{20}{30} \):
- Simplify \( \frac{20}{30} = \frac{2}{3} \)
- Prime factors of 3: \( 3 \)
- Contains prime factor 3.
-
Non-terminating
11. \( \frac{44}{60} \):
- Simplify \( \frac{44}{60} = \frac{11}{15} \)
- Prime factors of 15: \( 3 \times 5 \)
- Contains prime factor 3.
-
Non-terminating
12. \( \frac{10}{35} \):
- Simplify \( \frac{10}{35} = \frac{2}{7} \)
- Prime factors of 7: \( 7 \)
- Contains prime factor 7.
-
Non-terminating
13. \( \frac{45}{160} \):
- Simplify \( \frac{45}{160} = \frac{9}{32} \)
- Prime factors of 32: \( 2^5 \)
- Only prime factor is 2.
-
Terminating
14. \( \frac{35}{60} \):
- Simplify \( \frac{35}{60} = \frac{7}{12} \)
- Prime factors of 12: \( 2^2 \times 3 \)
- Contains prime factor 3.
-
Non-terminating
15. \( \frac{35}{100} \):
- Simplify \( \frac{35}{100} = \frac{7}{20} \)
- Prime factors of 20: \( 2^2 \times 5 \)
- Only prime factors are 2 and 5.
-
Terminating
16. \( \frac{8}{28} \):
- Simplify \( \frac{8}{28} = \frac{2}{7} \)
- Prime factors of 7: \( 7 \)
- Contains prime factor 7.
-
Non-terminating
Final Answer:
The terminating decimals are: 1, 4, 7, 8, 9, 13, 15.
Parent Tip: Review the logic above to help your child master the concept of ordering irrational rational numbers worksheet.
