Transfer the whole number from one form to the other --- this is the easiest part. For example, the fraction 3 35/147 will translate a decimal notation of three-point-something, and a decimal 5.137 will become, in fractional notation, 5 and a fraction.
Calculate the decimal from the fraction by dividing the denominator of the fraction into the numerator. For example 3 35/64 translates to 3.55 because 64 divided into 35 is 0.55.
Change a non-repeating decimal into a fraction by reducing the obvious fraction. For example 0.5 is really 5/10, 0.33 is really 33/100 and 0.147 is really 147/1,000. All you need to do to convert the decimal to a fraction is to reduce the obvious fraction. The good news is that powers of 10 --- like 10, 100 and 1,000 --- only have two and five as prime divisors. For example, 3.147 converts to 3 147/1,000 because 147 is not divisible by either two or five. On the other hand, 1.35 converts to 1 7/20 because 35/100 = (5 X 7) / (5 X 20) = 7/20.
Use a standard algebraic trick to convert a repeating decimal to a fraction. To convert 2.353535... --- the elipses means the 35 repeats --- to a fraction, let X = 0.353535..., so 100X = 35.353535..., and 100X - X = 35; so 99X = 35 and X = 35/99. Therefore 2.353535... converts to 2 35/99.