To determine whether the given fractions convert to repeating or terminating decimal numbers, we need to analyze their denominators after simplification.

Fraction $\frac{6}{7}$

• The fraction $\frac{6}{7}$ does not simplify further.
• The prime factorization of 7 is $7$, which is a prime number not equal to 2 or 5.

Since the denominator contains a prime factor other than 2 or 5, the decimal representation will be repeating.

Fraction $\frac{16}{25}$

• The fraction $\frac{16}{25}$ does not simplify further.
• The prime factorization of 25 is $5^2$, which only includes the prime factor 5.

Since the denominator only contains the prime factor 5, the decimal representation will be terminating.

Therefore:

• The fraction $\frac{6}{7}$ converts to a repeating decimal number.
• The fraction $\frac{16}{25}$ converts to a terminating decimal number.

So, the correct answers to fill in the blanks are:

• The fraction $\frac{6}{7}$ converts to a repeating decimal number.
• The fraction $\frac{16}{25}$ converts to a terminating decimal number.

Would you like further details or have any questions?

Here are 5 questions you might ask next:

1. How do you convert fractions to decimals manually?
2. What is the difference between repeating and terminating decimals?
3. How do you determine the type of decimal from a fraction?
4. Can you explain prime factorization in more detail?
5. What are examples of other fractions that convert to repeating or terminating decimals?

Tip: To determine if a fraction has a terminating decimal, check if the denominator (after simplification) only has the prime factors 2 or 5.