What is 3.83 repeating as a fraction?

Answer 1

To convert the repeating decimal 3.83 (with the 83 repeating) into a fraction, let ( x = 3.838383...). Multiply both sides by 100 to shift the decimal point two places: ( 100x = 383.8383...). Now, subtract the original ( x ) from this equation: ( 100x - x = 383.8383... - 3.8383...), which simplifies to ( 99x = 380). Therefore, ( x = \frac{380}{99} ), and the fraction can be simplified to ( \frac{380}{99} ).