how would you convert the repeating non terminating decimal to a fraction explain the process as you solve the problem 0.1515...
nonterminating decimal to a fraction
To convert a repeating non-terminating decimal to a fraction, you need to understand the concept of geometric series. Here's how you can solve the problem of converting 0.1515... to a fraction:
Step 1: Identify the repeating pattern
In this case, the pattern is "15" repeating. This pattern starts from the second decimal place.
Step 2: Set up the equation
Let's assume "x" represents the fraction equivalent of 0.1515... To get rid of the repeating pattern, we multiply x by 100, as there are two digits in the pattern (15), so it should be multiplied by 10^2 = 100:
100x = 15.1515...
Step 3: Subtract the equation
Next, we need to subtract the original equation from the equation obtained in step 2. This will eliminate the repeating pattern:
100x - x = 15.1515... - 0.1515...
Simplifying the equation gives:
99x = 15
Step 4: Solve for x
To find x, divide both sides of the equation by 99:
99x / 99 = 15 / 99
x = 15/99
Step 5: Simplify the fraction
To simplify the fraction further, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 3:
15 ÷ 3 / 99 ÷ 3
This simplifies to:
5/33
Therefore, the fraction equivalent of 0.1515... is 5/33.
Ms. Sue anyone help me please
0.1515=303\2000
let x = .151515...
there are 2 digits that repeat, so multiply each side by 100
(if 3 digits were to repeat, I would multiply by 1000 etc)
100x = 15.1515...
subtract the two equations
100x - x = 15.1515... - .1515...
99x = 15
x = 15/99 = 5/33
check with a calculator
If you had a case where there some non-repeating digits before the repeating digits follow the same method, but you will have to make an adjustment at the end
e.g. x = 0.23456456456...
multiply by 1000 since 3 digits repeat
1000x = 234.56456456...
again, subtract
999x = 234.330000... = 234.33
x = 234.33/999
= 23433/99900 , do you see what I just did ?
= 7811/33300