QuestionAugust 24, 2025

is (56)/(72) a terminating or repeating decimal? Repeating Decimal Terminating Decimal

is (56)/(72) a terminating or repeating decimal? Repeating Decimal Terminating Decimal
is (56)/(72) a terminating or repeating decimal?
Repeating Decimal
Terminating Decimal

Solution
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Answer

Repeating Decimal Explanation 1. Simplify the Fraction Simplify \frac{56}{72} by dividing both numerator and denominator by their greatest common divisor, which is 8. This gives \frac{7}{9}. 2. Determine Decimal Type A fraction in simplest form has a terminating decimal if its denominator (after simplification) has only the prime factors 2 and/or 5. The denominator 9 has the prime factorization 3^2, which means it is not composed of only 2s and 5s.

Explanation

1. Simplify the Fraction<br /> Simplify $\frac{56}{72}$ by dividing both numerator and denominator by their greatest common divisor, which is 8. This gives $\frac{7}{9}$.<br /><br />2. Determine Decimal Type<br /> A fraction in simplest form has a terminating decimal if its denominator (after simplification) has only the prime factors 2 and/or 5. The denominator 9 has the prime factorization $3^2$, which means it is not composed of only 2s and 5s.
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