# Question #9defc

May 6, 2016

see below

#### Explanation:

$\frac{13}{2}$= Finite decimal
$\frac{11}{3}$= Repeating decimal
$\frac{3}{5}$= Finite decimal
$\frac{15}{6}$= Finite decimal
$\frac{17}{7}$= Repeating decimal
$\frac{15}{8}$= Finite decimal

Every fraction is a rational number, so it cannot be an infinite decimal. Infinite decimal represent irrational numbers like $\sqrt{2}$

To check if a fraction is a finite or periodic (repeating) decimal you have to:

• simplify the fraction

• check the prime factorization of its denominator.

If the factorization consists only of $2$ and $5$ the fraction can be written as a finite decimal, else the fraction can be only written as a repeating (periodic) decimal.