Question

What is 0.12 with12 repeating

Answer 1

Answer:

4/33

Step-by-step explanation:

We seek to find the repeating decimal 0.121212... in the form of a fraction.

First, set x equal to this decimal:

x = 0.121212...

Multiply both sides by 100:

100x = 12.121212....

Now, let's subtract the original equation from this new one:

    100x = 12.121212....

-    x = 0.121212....

We realize that since the repeating decimal part goes on forever, we can simply cancel it out when we subtract. So we're left with:

100x - x = 12 - 0

99x = 12

Divide both sides by 99:

x = 12/99 = 4/33

The answer is 4/33.

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