Python Math: Convert a floating point number to an approximate rational value

Last update on May 28 2022 13:45:56 (UTC/GMT +8 hours)

Python Math: Exercise-47 with Solution

Write a Python program to convert a floating point number (PI) to an approximate rational value on the various denominator.

Note: max_denominator = 1000000

Sample Solution:-

Python Code:

import fractions
import math

print('PI       =', math.pi)

f_pi = fractions.Fraction(str(math.pi))
print('No limit =', f_pi)

for d in [1, 5,  50, 90, 100, 500, 1000000]:
    limited = f_pi.limit_denominator(d)
    print('{0:8} = {1}'.format(d, limited))

Sample Output:

PI       = 3.141592653589793                                                                                
No limit = 3141592653589793/1000000000000000                                                                
       1 = 3                                                                                                
       5 = 16/5                                                                                             
      50 = 22/7                                                                                             
      90 = 267/85                                                                                           
     100 = 311/99                                                                                           
     500 = 355/113                                                                                          
 1000000 = 3126535/995207

Flowchart:

$Flowchart: Convert a floating point number to an approximate rational value$

Python Code Editor:

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Python: Tips of the Day

Find current directory and file's directory:

To get the full path to the directory a Python file is contained in, write this in that file:

import os 
dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os
cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

The os and os.path modules.
The __file__ constant
os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")
os.path.dirname(path) (returns "the directory name of pathname path")
os.getcwd() (returns "a string representing the current working directory")
os.chdir(path) ("change the current working directory to path")

Ref: https://bit.ly/3fy0R6m