How you would convert the repeating, nonterminating decimal to a fraction? Explain the process as you solve the problem.
0.1515...
If you have 0.abc... where n digits repeat, then the fraction is
abc.../(n 9's)
In this case, 15/99
If x = 0.151515...
then
100x = 15.151515...
now subtract to get 99x = 15
Thank you so very much!! (:
To convert a repeating, nonterminating decimal to a fraction, we can follow a specific process. Let's solve the problem for the decimal 0.1515...
Step 1: Identify the repeating part
In this case, the repeating part is "15".
Step 2: Set up the equation
Let's call the decimal x. To set up the equation, we'll multiply x by a power of 10 to eliminate the repeating part. Since the repeating part consists of two digits (15), we'll multiply x by 100.
Step 3: Subtract the equation
Now, subtract the equation from step 2 from the original equation. This will help eliminate the repeating part.
100x - x = 15.1515... - 0.1515...
This simplifies to:
99x = 15
Step 4: Solve for x
Divide both sides of the equation by 99 to isolate x:
x = 15/99
Step 5: Simplify the fraction
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3 in this case:
x = (15/3) / (99/3)
x = 5/33
Therefore, the decimal 0.1515... can be converted to the fraction 5/33.