To determine whether the fraction [tex]\(\frac{5}{8}\)[/tex] produces a repeating decimal, let's follow these steps:
1. Convert the Fraction to Decimal:
To find the decimal representation of [tex]\(\frac{5}{8}\)[/tex], we perform the division [tex]\(5 \div 8\)[/tex].
[tex]\[
5 \div 8 = 0.625
\][/tex]
2. Determine if the Decimal is Repeating:
A repeating decimal is a decimal number that has digits that repeat infinitely after some initial non-repeating digits. In contrast, a terminating decimal stops after a finite number of digits.
The decimal representation [tex]\(0.625\)[/tex] clearly stops after three digits. Since [tex]\(0.625\)[/tex] does not have an infinitely repeating sequence of digits, it is considered a terminating decimal.
Therefore, the fraction [tex]\(\frac{5}{8}\)[/tex] does not produce a repeating decimal. The correct answer to the question is:
B. False
