Repeating decimal to a fraction rational definition
A repeating decimal is a decimal number in which one or more digits are repeated infinitely. To convert a repeating decimal to a fraction, you can use the following method:
Let x be the repeating decimal.
1. Let n = the number of non-repeating digits in x before the repeating part starts.
2. Let m = the number of digits in the repeating part of x.
3. Write down x in the form:
x = a + b,
where a is the non-repeating part and b is the repeating part.
4. Multiply both sides of the equation by 10^n to get:
10^n * x = 10^n * a + b.
5. Subtract the equation in step 3 from the equation in step 4 to get:
(10^n - 1) * x = 10^n * a - a = 9a.
6. Solve for x to get:
x = b / (10^m - 1).
7. Convert x to a fraction by writing it as b / (10^m - 1) and simplify if possible.
This process allows you to convert a repeating decimal into a fraction, making it a rational number.