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Whats the answer to that question?

Whats the answer to that question?-example-1
User Soryngod
by
8.4k points

1 Answer

1 vote

Answer:

-0.9090... can be written as
(10)/(11).

Step-by-step explanation:

Any repeating decimal can be written as a fraction by dividing the section of the pattern to be repeated by 9's.

We can start by listing out

0.909090... = 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...

Now. we let this series be equal to x, that is


x = 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...

Now, we'll multiply both sides by 100 .


100x = 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + ...

Then, subtract the 1st equation from the second like so:


100x = 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...


-x = - 9/10 - 0/100 - 9/1000 - 0/10000 - 9/100000 - 0/1000000 - ...

And we end up with this:


99x=90

Finally, we divide both sides by 99 in order to isolate x and get the fraction we're looking for.


x=(90)/(99)

Which can be reduced and simplified to


x=(10)/(11)

Hope this helps!

User ManWithSleeve
by
8.6k points

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