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Express the repeating decimal as the ratio of two integers. (13)=0.131313dots

User Ironsun
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Final answer:

The repeating decimal 0.131313... can be expressed as the ratio 13/99 by using an algebraic method where the repeating pattern of the decimal is isolated and then subtracted to find the ratio.

Step-by-step explanation:

To express the repeating decimal 0.131313... as the ratio of two integers, we can use a simple algebraic method. Let's define the repeating decimal as x:

x = 0.131313...

Multiplying both sides of the equation by 100, since the repeat is two digits long, gives us:

100x = 13.131313...

Now we subtract the original x from this to get the following:

100x - x = 13.131313... - 0.131313...

99x = 13

Dividing both sides by 99 gives us:

x = 13 / 99

Therefore, the repeating decimal 0.131313... is represented as the ratio 13/99 which is in the form of two integers.

User Eng Yew
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