Question
alan rewrites a fraction less than 1 as a decimal. The numerator is a whole number greater than 0. For which denominator will the fraction convert to a terminating decimal?
a. 13
b. 9
c. 16
d. 12
a. 13
b. 9
c. 16
d. 12
Answers
GPT-4o mini
A fraction in its simplest form will convert to a terminating decimal if its denominator (after simplifying) has no prime factors other than 2 and 5. Let's analyze the given options:
a. 13
- Prime factorization: \( 13 \) (not 2 or 5)
- **Not a terminating decimal**.
b. 9
- Prime factorization: \( 3^2 \) (not 2 or 5)
- **Not a terminating decimal**.
c. 16
- Prime factorization: \( 2^4 \) (only includes 2)
- **Is a terminating decimal**.
d. 12
- Prime factorization: \( 2^2 \times 3 \) (includes 3 which is not 2 or 5)
- **Not a terminating decimal**.
From the analysis, the denominator that will convert a fraction to a terminating decimal is:
**c. 16**.
a. 13
- Prime factorization: \( 13 \) (not 2 or 5)
- **Not a terminating decimal**.
b. 9
- Prime factorization: \( 3^2 \) (not 2 or 5)
- **Not a terminating decimal**.
c. 16
- Prime factorization: \( 2^4 \) (only includes 2)
- **Is a terminating decimal**.
d. 12
- Prime factorization: \( 2^2 \times 3 \) (includes 3 which is not 2 or 5)
- **Not a terminating decimal**.
From the analysis, the denominator that will convert a fraction to a terminating decimal is:
**c. 16**.