Computer Science - Coding in Python

Converting a decimal to a fraction

Although computers generally represent numbers as decimals, it is often convenient to express values as fractions. If we desire to convert a decimal to a fraction, we need to follow a two-step process:

Starting with the number itself, multiply by ten repeatedly until no values remain after the decimal point. This is the numerator. Keep the multiplier as the denominator.

Simplify the fraction.

For instance, for 0.75:

Multiply by ten repeatedly:

0.751010=750.751010=75

Thus the numerator is 75 and the denominator is 1010=1001010=100.

Simplify the fraction:

Find the factors of the numerator and the denominator.

75?{1,3,5,25,75}100?{1,2,4,5,10,20,25,50,100}75?{1,3,5,25,75}100?{1,2,4,5,10,20,25,50,100}

Find the greatest common factor of each and divide both by it.

7525=310025=47525=310025=4

0.75?340.75?34

Write a function factors( n ) which accepts a number n and returns a list containing all of the factors of that number. (This is a common task. Write your own codedon't just google it!)

Write a function fraction( n ) which accepts a decimal number n and returns a tuple ( numerator,denominator ) of the resulting fraction representation.

Your submission should include two functions factors( n ) and fraction( n ).

STARTER CODE:

def factors( n ): pass

def fraction( n ): n_str = str( n ) decimal_part = n_str[ n_str.find( '.' )+1: ] # 1. Multiply by ten repeatedly (to make all of decimal positive). numer = n * 10 ** ??? denom = ???

# 2. Find factors. numer_factors = ??? denom_factors = ??? factor = 1 # ??? find greatest common factor of both numerator and denominator # ??? divide both by GCF before returning them return ( numer,denom )