Respuesta :

konrad509

[tex] 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}
[/tex]

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or using this weird notation
[tex] 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}[/tex]

Answer

[tex] \frac{7}{37} [/tex]


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.


[tex] \frac{189}{999} [/tex]


We could simplify the answer!

[tex] \frac{189}{999} [/tex]


Therefore, the answer would simply be [tex] \frac{7}{37} [/tex]

[tex] \frac{7}{37} [/tex]


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.

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