Question

Which of the following fractions will terminate when expressed as a decimal? (Choose all that apply.)

• A. $\frac{1}{256}$
• B. $\frac{27}{100}$
• C. $\frac{100}{27}$
• D. $\frac{231}{660}$
• E. $\frac{7}{105}$

Answer 1

Answer: (A), (B), (D)

$\frac{1}{256}$
$\frac{231}{660}$
$\frac{27}{100}$

Recall that in order for the decimal expansion of a fraction to terminate, the fraction's denominator, in fully reduced form, must have a prime factorization that consists of only $2$'s and/or $5$'s.

The denominator in $A$ is composed of only $2$'s, $(256=2^8)$.

The denominator in $B$ is composed of only $2$'s and $5$'s, $(100=2^2\times 5^2)$.

In fully reduced form, the fraction in $D$ is equal to $\frac{7}{20}$ and the denominator $20$ is composed of only $2$'s and $5$'s $(20=2^2\times 5)$.

By contrast, the denominator in $C$ has prime factors other than $2$'s and $5$'s $(27=3^3)$, and in fully reduced form, the fraction in $E$ is equal to $\frac{1}{15}$, and $15$ has a prime factor other than $2$'s and $5$'s $(15=3\times 5)$.

Therefore, options $A$, $B$ and $D$ are the correct answers.