How would you convert the repeating nonterminating decimal to a fraction? Explain the process as you solve the problem. 0.1515
To convert a repeating nonterminating decimal to a fraction, we need to follow a specific process. Let's solve the problem step by step for the decimal 0.1515.
Step 1: Assign a variable to the repeating part
In this case, the repeating part is '15'. Let's assign it the variable 'x'.
Step 2: Create an equation for the repeating part
To create an equation, we multiply the repeating part 'x' by the power of 10 that has the same number of digits as 'x'. Since 'x' has two digits, we multiply it by 100 (10^2).
So, 100x = 15.1515
Step 3: Subtract the original number
We subtract the original number (0.1515) from the equation we just created to eliminate the repeating part:
100x - x = 15.1515 - 0.1515
99x = 15
Step 4: Solve for 'x'
To solve for 'x', we divide both sides of the equation by 99:
99x / 99 = 15 / 99
x = 15/99
Step 5: Simplify the fraction (if possible)
To simplify the fraction 15/99, we find the greatest common divisor (GCD) of the numerator and denominator, which is 3 in this case. Dividing both the numerator and denominator by 3, we get:
x = (15/3) / (99/3)
x = 5/33
Therefore, the repeating nonterminating decimal 0.1515 can be converted to the fraction 5/33.