Questionf. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. as a terminating derimal is (Type an integer or a decimal.) B. cannot be written as a terminating decimal.
Studdy Solution
STEP 1
1. A fraction can be expressed as a terminating decimal if its denominator can be expressed as a product of the prime factors 2 and/or 5 only.
2. We need to determine if can be expressed as a terminating decimal.
STEP 2
1. Factor the denominator.
2. Determine if the denominator can be expressed using only the prime factors 2 and/or 5.
3. Conclude whether the fraction can be expressed as a terminating decimal.
STEP 3
Factor the denominator .
STEP 4
Recognize that .
STEP 5
Check if the denominator can be expressed using only the prime factors 2 and/or 5.
Since , it is expressed using only the prime factor 5.
STEP 6
Conclude that can be expressed as a terminating decimal because its denominator is a power of 5.
The correct choice is:
A. as a terminating decimal is .
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