How would you convert the repeating nontermonating decimal to a fraction? Explain the process as you solve the problem 0.1515

I put 1515/10000 and got 303/2000

Right?

Ms. Sue i dont want to be rude but... do you even know how to do this ?

To convert a repeating non-terminating decimal to a fraction, we can use the concept of geometric series.

Let's take the decimal 0.1515 as an example. To convert it to a fraction, we'll assume that the decimal part (1515) repeats indefinitely.

Step 1: Determine the variable for the repeating decimal
Let x be the repeating decimal 0.1515.

Step 2: Multiply the decimal by a power of 10 to eliminate the repeating part
We need to multiply x by a power of 10 to shift the decimal point so that the repeating part lines up. Since there are two digits after the decimal point that repeat, we multiply x by 100:

100x = 15.1515

Step 3: Subtract the original decimal from the result obtained in Step 2
To eliminate the repeating part, we subtract x from 100x:

100x - x = 15.1515 - 0.1515
99x = 15

Step 4: Solve for x
To isolate x, we divide both sides of the equation by 99:

x = 15 / 99

Step 5: Simplify the fraction (if possible)
In this case, 15 and 99 have a common factor of 3, so we can simplify further:

x = 5 / 33

Therefore, the repeating non-terminating decimal 0.1515 can be expressed as the fraction 5/33.