How would you convert the repeating nondeterminating decimal into a fraction? 0.151515...

0.15151515... =

15 / 100 + 15 / 10000 + 15 / 1000000 + 15 / 100000000 + ... =

15 / 100 + 15 / 100 ^ 2 + 15 / 100 ^ 3 + 15 / 100 ^ 4 + ...

This is the geometric series :

a + a r + a r ^ 2 + a r ^ 3 + a r ^ 4 + ...

with a = 15 / 100 and r = 1 / 100

As n goes to infinity the sum of the geometric series are :

S = a / ( 1 - r )

In this case :

a = 15 / 100 , r = 1 / 100 so :

S = a / ( 1 - r )

S = ( 15 / 100 ) / ( 1 - 1 / 100 ) =

( 15 /100 ) / ( 100 / 100 - 1 / 100 ) =

( 15 / 100 ) / ( 99 / 100 ) =

15 * 100 / ( 99 * 100 ) = 15 / 99

0.15151515... = 15 / 99

0.15151515... = 15 / 99 = 3 * 5 / ( 3 * 33 ) = 5 / 33

To convert the repeating nonterminating decimal 0.151515... into a fraction, you can follow these steps:

Step 1: Let's represent the repeating decimal as x: 0.151515...
Step 2: Multiply x by a power of 10 that eliminates the repeating part. In this case, it would be 100x: 100x = 15.151515...
Step 3: Subtract x from 100x: 100x - x = 15.151515... - 0.151515...
This will eliminate the repeating part, leaving only the non-repeating part on the right side of the equation.
Simplifying further, 100x - x = 15.151515... - 0.151515... becomes 99x = 15.
Step 4: Solve the equation for x: divide both sides of the equation by 99: 99x/99 = 15/99.
Simplifying further, x = 15/99.
Step 5: Simplify the fraction if possible. In this case, we can divide the numerator and denominator by 3 to simplify: 15/99 = 5/33.

Therefore, the repeating nonterminating decimal 0.151515... is equivalent to the fraction 5/33.

To convert a repeating non-terminating decimal into a fraction, you can follow these steps:

Step 1: Assign a variable to the repeating decimal part.
Let's say the repeating part is denoted as 'x'.

Step 2: Determine the number of repeating digits.
Looking at the given decimal, we can see that there are 2 repeating digits (15).

Step 3: Set up the equation.
Since the repeating part 'x' consists of two digits, we need to multiply it by 100 (10^2) to shift the decimal point. This allows us to eliminate the repeating part.
0.151515... multiplied by 100 will be 15.151515...

Step 4: Subtract the original equation.
Now, we subtract the original equation from the equation in Step 3:
100x - x = 15.151515... - 0.151515...
Simplifying this equation gives us:
99x = 15

Step 5: Solve for 'x'.
Dividing both sides of the equation by 99, we get:
x = 15/99

Step 6: Simplify the fraction.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 99 is 3.
Therefore, the simplified fraction is:
15/99 = 5/33

So, the decimal 0.151515... is equivalent to the fraction 5/33.