How to resolve the algorithm Convert decimal number to rational step by step in the VBA programming language

Published on 12 May 2024 09:40 PM
#Vba

How to resolve the algorithm Convert decimal number to rational step by step in the VBA programming language

Table of Contents

Problem Statement

The task is to write a program to transform a decimal number into a fraction in lowest terms. It is not always possible to do this exactly. For instance, while rational numbers can be converted to decimal representation, some of them need an infinite number of digits to be represented exactly in decimal form. Namely, repeating decimals such as 1/3 = 0.333... Because of this, the following fractions cannot be obtained (reliably) unless the language has some way of representing repeating decimals: Acceptable output: Finite decimals are of course no problem:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Convert decimal number to rational step by step in the VBA programming language

Source code in the vba programming language

Function Real2Rational(r As Double, bound As Long) As String

If r = 0 Then
    Real2Rational = "0/1"
ElseIf r < 0 Then
    Result = Real2Rational(-r, bound)
    Real2Rational = "-" & Result
Else
    best = 1
    bestError = 1E+99
    For i = 1 To bound + 1
        currentError = Abs(i * r - Round(i * r))
        If currentError < bestError Then
            best = i
            bestError = currentError
            If bestError < 1 / bound Then GoTo SkipLoop
        End If
    Next i
SkipLoop:
    Real2Rational = Round(best * r) & "/" & best
End If
End Function

Sub TestReal2Rational()
Debug.Print "0.75" & ":";
For i = 0 To 5
    Order = CDbl(10) ^ CDbl(i)
    Debug.Print " " & Real2Rational(0.75, CLng(Order));
Next i
Debug.Print

Debug.Print "0.518518" & ":";
For i = 0 To 5
    Order = CDbl(10) ^ CDbl(i)
    Debug.Print " " & Real2Rational(0.518518, CLng(Order));
Next i
Debug.Print

Debug.Print "0.9054054" & ":";
For i = 0 To 5
    Order = CDbl(10) ^ CDbl(i)
    Debug.Print " " & Real2Rational(0.9054054, CLng(Order));
Next i
Debug.Print

Debug.Print "0.142857143" & ":";
For i = 0 To 5
    Order = CDbl(10) ^ CDbl(i)
    Debug.Print " " & Real2Rational(0.142857143, CLng(Order));
Next i
Debug.Print

Debug.Print "3.141592654" & ":";
For i = 0 To 5
    Order = CDbl(10) ^ CDbl(i)
    Debug.Print " " & Real2Rational(3.141592654, CLng(Order));
Next i
Debug.Print

Debug.Print "2.718281828" & ":";
For i = 0 To 5
    Order = CDbl(10) ^ CDbl(i)
    Debug.Print " " & Real2Rational(2.718281828, CLng(Order));
Next i
Debug.Print

Debug.Print "-0.423310825" & ":";
For i = 0 To 5
    Order = CDbl(10) ^ CDbl(i)
    Debug.Print " " & Real2Rational(-0.423310825, CLng(Order));
Next i
Debug.Print

Debug.Print "31.415926536" & ":";
For i = 0 To 5
    Order = CDbl(10) ^ CDbl(i)
    Debug.Print " " & Real2Rational(31.415926536, CLng(Order));
Next i
End Sub

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