Select the correct answer from each drop-down menu.
Do the fractions 6/7
 and 16/25
 convert to repeating or terminating decimal numbers?
The fraction 6/7
 converts to a 
 decimal number, and 16/25
 converts to a 
 decimal number.

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.

Explore how fractions convert to decimal numbers, focusing on determining whether a fraction results in repeating or terminating decimals. Example fractions include 6/7 and 16/25, analyzed through their prime factorization and mathematical properties. Suitable for students in Grades 6-8.

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