Imports System
Imports System.Numerics
'
' DecimalToRational
' -----------------
' Converts a decimal number (given as a string) into a rational number p/q.
'
' Why parse the string?
' • VB.NET has no built‑in rational type.
' • Double/Single cannot preserve exact decimal digits.
' • Using strings + BigInteger ensures perfect accuracy.
'
' Algorithm:
' 1. Look for a decimal point.
' 2. If none → integer → numerator = n, denominator = 1.
' 3. Otherwise:
' Example: "12.345"
' integer part = 12
' fractional part = 345
' digits = 3
'
' numerator = integer_part * 10^digits + fractional_part
' denominator = 10^digits
'
' 4. Reduce using gcd.
'
Module DecimalToRational
' Simple container for numerator/denominator
Structure Rational
Public Numerator As BigInteger
Public Denominator As BigInteger
Public Overrides Function ToString() As String
Return Numerator.ToString() & "/" & Denominator.ToString()
End Function
End Structure
' Convert decimal string to Rational
Function ConvertDecimalToRational(s As String) As Rational
Dim dotPos As Integer = s.IndexOf("."c)
If dotPos = -1 Then
' No decimal point → integer
Dim num As New BigInteger(Long.Parse(s))
Return New Rational With {.Numerator = num, .Denominator = BigInteger.One}
End If
' Split into integer and fractional parts
Dim intPart As String = s.Substring(0, dotPos)
Dim fracPart As String = s.Substring(dotPos + 1)
Dim integerValue As New BigInteger(Long.Parse(intPart))
Dim fractionalValue As New BigInteger(Long.Parse(fracPart))
Dim digits As Integer = fracPart.Length
' Build denominator = 10^digits
Dim denominator As BigInteger = BigInteger.Pow(10, digits)
' Build numerator
Dim numerator As BigInteger = integerValue * denominator + fractionalValue
' Reduce using gcd
Dim g As BigInteger = BigInteger.GreatestCommonDivisor(numerator, denominator)
numerator = numerator / g
denominator = denominator / g
Return New Rational With {.Numerator = numerator, .Denominator = denominator}
End Function
Sub Main()
Dim values() As String = {
"3.5", "12.75", "0.125", "100.001",
"7", "42.0", "0.333", "5.2"
}
For Each v In values
Dim r As Rational = ConvertDecimalToRational(v)
Console.WriteLine(v & " -> " & r.ToString())
Next
End Sub
End Module
' run:
'
' 3.5 -> 7/2
' 12.75 -> 51/4
' 0.125 -> 1/8
' 100.001 -> 100001/1000
' 7 -> 7/1
' 42.0 -> 42/1
' 0.333 -> 333/1000
' 5.2 -> 26/5
'
