To determine whether the fraction [tex]\(\frac{7}{14}\)[/tex] represents a terminating decimal, let’s go through the reasoning step-by-step.
1. Simplify the Fraction: First, we simplify [tex]\(\frac{7}{14}\)[/tex].
[tex]\[
\frac{7}{14} = \frac{7 \div 7}{14 \div 7} = \frac{1}{2}
\][/tex]
2. Determine if the Simplified Fraction is a Terminating Decimal:
- For a fraction [tex]\(\frac{a}{b}\)[/tex] to be a terminating decimal, the denominator [tex]\(b\)[/tex] (when in its simplest form) must have only the prime factors 2 and/or 5.
3. Analyze the Denominator:
- In our simplified fraction [tex]\(\frac{1}{2}\)[/tex], the denominator is 2.
- Since 2 is a prime factor that satisfies the conditions for a terminating decimal (as it is either 2 or 5),
Thus, the fraction [tex]\(\frac{7}{14}\)[/tex], which simplifies to [tex]\(\frac{1}{2}\)[/tex], does indeed represent a terminating decimal.
Given the provided information, the correct answer to the question "Does [tex]\(\frac{7}{14}\)[/tex] represent a terminating decimal?"
The answer is:
Yes.
