To determine whether the fraction [tex]\(\frac{1}{5}\)[/tex] represents a terminating decimal, we need to examine the denominator of the fraction once it is expressed in its simplest form.
A fraction will have a terminating decimal if, after simplifying, the only prime factors of its denominator are 2 and/or 5. Let's break this down step-by-step:
1. Identify the fraction:
[tex]\[
\frac{1}{5}
\][/tex]
In this case, the numerator is 1 and the denominator is 5.
2. Simplify the fraction:
The fraction [tex]\(\frac{1}{5}\)[/tex] is already in its simplest form because 1 and 5 have no common divisors other than 1.
3. Check the prime factors of the denominator:
The denominator is 5. We need to determine the prime factors of 5. A prime factor is any prime number that divides another number exactly.
- The number 5 is a prime number itself. Therefore, the only prime factor of 5 is 5.
4. Determine if the prime factors are 2 or 5:
Since the only prime factor of the denominator (5) is 5, we see that the denominator contains only the prime factor 5.
Since the denominator's prime factors are either 2 or 5 (in this case, just 5), the fraction [tex]\(\frac{1}{5}\)[/tex] does indeed represent a terminating decimal.
Thus, the correct answer is:
Yes
