Question

Could someone PLEASE just HELP me with this question.

Answer 1

Answer

$\frac{7}{37}$

Detailed Explanation

To simply answer this, since .189 has three digits we are going to be inserting 999 as the denominator since it is a repeating decimal.

$\frac{189}{999}$

We could simplify the answer!

$\frac{189}{999}$

Therefore, the answer would simply be $\frac{7}{37}$

$\frac{7}{37}$

Always Remember

In the future, always remember whenever you have a three digit decimal and the problem asks you to convert it into a fraction, you should always insert 1000 as the denominator (the numerator is basically the decimal without the decimal point) and simplify if necessary.

Answer 2

$x=0.\overline{189}\\ 1000x=189.\overline{189}\\ 1000x-x=189.\overline{189}-0.\overline{189}\\ 999x=189\\ x=\dfrac{189}{999}=\dfrac{7}{37}$

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or using this weird notation
$x=0.\dot{1}8\dot{9}\\ 1000x=189.\dot{1}8\dot{9}\\ 1000x-x=189.\dot{1}8\dot{9}-0.\dot{1}8\dot{9}\\ 999x=189\\ x=\dfrac{189}{999}=\dfrac{7}{37}$