9. how you would convert the repeating, non terminating decimal to a fraction? explain the process as you solve the problem. 0.1515

I don't understand this question can someone help explain this?

How did u get that

I know the answer but how do u get that answer

so what's the correct answer?

300.700 The decimal is 0.1515 but the fraction is 303/2000.

Certainly! Converting a repeating, non-terminating decimal to a fraction involves understanding the concept of infinite repeating decimals and using algebraic equations.

Let's solve the problem step by step with the input value: 0.1515

Step 1: Identify the repeating pattern
In this case, we see that "15" is repeating. So, the repeating pattern is "15".

Step 2: Assign variables to the repeating part
Since our repeating pattern has two digits, we can assign a variable, let's say "x", to represent it. So, x = 15.

Step 3: Create an equation
To eliminate any decimals, we need to shift the decimal point in an appropriate manner. Since there are two digits in the repeating pattern, we multiply x by 100 to shift it two places to the left. Therefore, 100x = 1515.

Step 4: Subtract the original equation from the shifted equation
We subtract the equation from step 3 by the equation in step 2 to eliminate the repeating part. In this case, it would be:
100x - x = 1515 - 0.15

This simplifies to:
99x = 1514.85

Step 5: Solve for x
To solve for x, divide both sides of the equation by 99:
x = 1514.85 / 99

Step 6: Simplify the fraction
Finally, we simplify the fraction. In this case, the fraction would be:
1514.85 / 99

This can be further simplified by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by the GCD.

Therefore, the conversion of the repeating decimal 0.1515 to a fraction is 1514.85 / 99, which can be simplified further if necessary.