The problem asks to select all fractions that are equivalent to terminating decimals. For a fraction to represent a terminating decimal, its denominator must have only the prime factors 2 and/or 5 (since terminating decimals occur when the fraction can be written as a fraction of powers of 2 or 5 in the denominator).

Let's evaluate each of the fractions given:

1. $\frac{9}{20}$:

   • The prime factorization of 20 is $2^2 \times 5$. Since the denominator only contains the prime factors 2 and 5, this fraction represents a terminating decimal.

2. $\frac{1}{35}$:

   • The prime factorization of 35 is $5 \times 7$. Since 7 is not a prime factor of 2 or 5, this fraction does not represent a terminating decimal.

3. $\frac{14}{35}$:

   • The prime factorization of 35 is the same as in the previous case, $5 \times 7$. This means this fraction also does not represent a terminating decimal.

4. $\frac{1}{16}$:

   • The prime factorization of 16 is $2^4$. Since it only contains the prime factor 2, this fraction represents a terminating decimal.

Conclusion:

The fractions that represent terminating decimals are:

• $\frac{9}{20}$
• $\frac{1}{16}$

Would you like more details or have any other questions?

Here are five related questions to deepen your understanding:

1. Why do only the factors 2 and 5 in the denominator result in a terminating decimal?
2. How can you convert a fraction into its decimal form to check if it's terminating?
3. Can you give examples of fractions that result in repeating decimals and explain why?
4. How do you simplify fractions to check their prime factors?
5. What happens if a fraction has both terminating and repeating parts in its decimal expansion?

Tip: To check if a fraction has a terminating decimal, focus on the prime factorization of the denominator—if it only contains 2s and 5s, the decimal will terminate.