Without dividing, determine which of the following represent terminating decimals. a. \( \frac{20}{24} \) b. \( \frac{21}{28} \) a. Is \( \frac{20}{24} \) a terminating decimal? A. No, because the only factors of the denominator, 24 , are 2 and 5 . B. No, the denominator of the simplified fraction contains a factor other than 2 or 5 . C. Yes, because the only factors of the denominator, 24 , are 2 and 5 . D. Yes, the only factors of the denominator of the simplified fraction are 2 or 5 .

To determine if a fraction results in a terminating decimal, a key consideration is its simplified denominator. If the simplified form of the fraction's denominator contains only the prime factors 2 and/or 5, then the decimal representation will terminate. When simplifying \( \frac{20}{24} \), it reduces to \( \frac{5}{6} \). The denominator 6 has a prime factor of 3, which signifies that the decimal representation will not terminate. Now, onto the other fraction. The fraction \( \frac{21}{28} \) simplifies to \( \frac{3}{4} \); the denominator 4 consists solely of the prime factor 2. Hence, \( \frac{21}{28} \) will result in a terminating decimal. So, the answer regarding \( \frac{20}{24} \): B. No, the denominator of the simplified fraction contains a factor other than 2 or 5. For \( \frac{21}{28} \), it is indeed a terminating decimal since its simplified version's denominator only contains 2. Now, let’s chat about fun facts! Determining whether a decimal terminates can often feel like a math mystery, but it involves some simple prime factor sleuthing! Factors really are the secret agents of numbers, and understanding their behavior can lead you to the conclusion about decimals. If you're curious about further exploration, dive into the world of rational numbers and explore how fractions can be converted to decimals through decimal expansion. Websites or videos on long division and decimal conversion can spark your imagination and solidify your understanding!