Without dividing, determine which of the following represent terminating decimals.
a.
b.

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 . 2

b. Is a terminating decimal?

A. Yes, the only factors of the denominator of the simplified fraction are 2 or 5 . .

B. No, because the only factors of the denominator, 28 , are 2 and 5 .

C. Yes, because the only factors of the denominator, 28 , are 2 and 5 .

D. No, the denominator of the simplified fraction contains a factor other than 2 or 5 . 2

Ask by Tyler Conner. in the United States

Mar 22,2025

Question

Without dividing, determine which of the following represent terminating decimals.
a.
b.

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 . 2

b. Is a terminating decimal?

A. Yes, the only factors of the denominator of the simplified fraction are 2 or 5 . .

B. No, because the only factors of the denominator, 28 , are 2 and 5 .

C. Yes, because the only factors of the denominator, 28 , are 2 and 5 .

D. No, the denominator of the simplified fraction contains a factor other than 2 or 5 . 2

Ask by Tyler Conner. in the United States

Mar 22,2025

UpStudy AI · Accepted Answer

We first recall that a fraction represents a terminating decimal if and only if, once simplified, its denominator has no prime factors other than 2 or 5.

**Problem a.** Consider the fraction

$$
\frac{20}{24}.
$$

1. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor. The GCD of 20 and 24 is 4, so

$$
\frac{20}{24} = \frac{20 \div 4}{24 \div 4} = \frac{5}{6}.
$$

2. Next, factor the simplified denominator:

$$
6 = 2 \times 3.
$$

3. Since there is a factor 3 in the denominator, which is neither 2 nor 5, the fraction $$\frac{5}{6}$$ does not represent a terminating decimal.

**Problem b.** Now consider the fraction

$$
\frac{21}{28}.
$$

1. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor. The GCD of 21 and 28 is 7, so

$$
\frac{21}{28} = \frac{21 \div 7}{28 \div 7} = \frac{3}{4}.
$$

2. Factor the simplified denominator:

$$
4 = 2 \times 2 = 2^2.
$$

3. Here, the only prime factor in the denominator is 2, which is allowed because it is among the factors 2 or 5. Therefore, $$\frac{3}{4}$$ represents a terminating decimal.

**Final Answers:**

- For $$\frac{20}{24}$$: No, it does not represent a terminating decimal.
- For $$\frac{21}{28}$$: Yes, it represents a terminating decimal.
- $$\frac{20}{24}$$ does not represent a terminating decimal. - $$\frac{21}{28}$$ represents a terminating decimal.

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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 .	2
b. Is a terminating decimal?
A. Yes, the only factors of the denominator of the simplified fraction are 2 or 5 .	.
B. No, because the only factors of the denominator, 28 , are 2 and 5 .
C. Yes, because the only factors of the denominator, 28 , are 2 and 5 .
D. No, the denominator of the simplified fraction contains a factor other than 2 or 5 .	2