show the steps for changing the repeating decimal, with is rational, to a radio or fraction.
0.523523...= what fraction?
To convert the repeating decimal 0.523523... to a fraction, we can use a basic algebraic method for dealing with repeating decimals.
Let's represent the repeating decimal as "x" and multiply it by a power of 10 to create a whole number.
Step 1: Multiply the repeating decimal (x) by a power of 10 that moves the decimal point so that the repeating part aligns with the non-repeating part. Since there are 3 non-repeating digits before the repeating part, multiply x by 1000:
1000x = 523.523523...
Step 2: Subtract the original repeating decimal (x) from the result of the previous step to eliminate the repeating part:
1000x - x = 523.523523... - 0.523523...
999x = 523
Step 3: Solve for x:
x = 523/999
Therefore, the fraction equivalent to the repeating decimal 0.523523... is 523/999.