Who do u change numbers with a repeating decimal into a fraction?

what is 87.55555555555555555555 and how would a figure that out myself? Is there a calutor that can do repeating demicals?Who do u change numbers with a repeating decimal into a fraction?
Never fear, Jaws is here!





You don't need any sort of calculator to do this, because repeating decimals are rational numbers, which means they can be converted to a fraction through a mathematical process. Here is the process.





1. Let N = the number





2. Set up an equation with N set equal to the number.





3. Multiply both sides by 10^n, where n represents the number of unique repeating decimals.





4. Subtract N from both sides and then solve as a proportion.





All right, let's get started.





Let N = 87.555...





So now we set up our equation:





N = 87.555...





Now, according to step three, we need to multiply both sides by 10^n, where n represents the number of unique repeating digits. In this case, there is only one repeating digit, 5. Therefore, we multiply both sides by 10^1, or just 10.





10N = 875.555...





Now we subtract N from both sides:





10N - N = 875.555... - 87.555...





However, on one side we continue to express 'N' as a variable, whereas on the other side we are using the actual value of N. Now the repeating decimals will cancel each other out, and you will be left with a whole number:





10N - N = 875.555... - 87.555...





9N = 788





N = 788/9





Now we know that N = 87.555... and we also know that N = 788/9. Therefore, by substitution, we can say that:





87.555... = 788/9