Question

Write a Python 3 code that takes an irrational number 'x' and return 'm' fraction approximations. For example let x=pi and m=4, then the program should return 4 examples of pi written as a fraction approximation.  

Answer 1

The code which takes an irrational number x and returns the given number of fraction approximations is given below and will be explained below -

from fractions import Fraction
import math

x = float(input('Enter irrational number: '))
m = int(input('Enter number of fraction approximations: '))

c=10

for i in range(1,m+1):
    res = Fraction(x).limit_denominator(int(math.pow(c,i)))
    print(res)

Explanation -

• Import the fraction and math libraries.
• Take x and m as inputs. x will be a float as it is a decimal and m will be an integer.
• Initialize a variable to 10.
• Now, we run a loop from 1 to m, i.e if m=4, the loop will run from 1,2,3, and 4.
• The line Fraction(x) converts a decimal to a fraction. But it can give very large fractions. So we use limit_denominator so that denominator is set to a small value. The value which we have chosen is 10,100,1000 and so on. To calculate that we use math.pow function.
• We print the fraction value at each step.

Output -

As it is seen in the output screenshot, the entered irrational number is pi(3.141592) and I want 4 function approximations. Now if you see the output, we have the denominators limited to 10,100,1000 and so on. So the first approximation comes out to be 22/7 which is expected.