Question

you are given a fraction in simplest form.the numerator is not zero. when you write the fraction as a decimal,it is a repeating decimal.which numbers from 1 to 10 could be the denominator​

Answer 1

You are given a fraction in simplest form. The possible denominators are 3, 6, 7, 9

Solution:

Given that, You are given a fraction in simplest form.

The numerator is not zero. When you write the fraction as a decimal, it is a repeating decimal.

We have to find which numbers from 1 to 10 could be the denominator

Now, let us check each number by considering the numerator as 1

Then,  

$1 \rightarrow \frac{1}{1}=1$ ⇒ non repeating

$2 \rightarrow \frac{1}{2}=0.5$ ⇒ non repeating

$3 \rightarrow \frac{1}{3}=0.333333333333$ ⇒ repeating

$4 \rightarrow \frac{1}{4}=0.25$ ⇒ non repeating

$5 \rightarrow \frac{1}{5}=0.2$ ⇒ non repeating

$6 \rightarrow \frac{1}{6}=0.1666666666666$ ⇒ repeating

$7 \rightarrow \frac{1}{7}=0.1428571428571$ ⇒ repeating

$8 \rightarrow \frac{1}{8}=0.125$ ⇒ non repeating

$9 \rightarrow \frac{1}{9}=0.11111111111111$ ⇒ repeating

$10 \rightarrow \frac{1}{10}=0.1$ ⇒ non repeating

If we want to test with any other numerator. Suppose 5, then numerator is 5 x 1, which means 5 divided by denominator equals with 5 x 1 divided by denominator. So its again product of the numerator we want and above values, then, non repeating stays non repeating and repeating stays repeating.

Hence, the possible denominators are 3, 6, 7, 9