Round #634

Convert 0.625 to a fraction in lowest terms.

To convert the decimal 0.625 to a fraction in its lowest terms, follow these steps: 1. **Express the decimal as a fraction**: \[ 0.625 = \frac{625}{1000} \] 2. **Simplify the fraction**: - Find the greatest common divisor (GCD) of 625 and 1000. - The prime factorization of 625 is \(5^4\). - The prime factorization of 1000 is \(2^3 \times 5^3\). - The GCD is the product of the lowest powers of common prime factors, which is \(5^3 = 125\). 3. **Divide both the numerator and the denominator by the GCD**: \[ \frac{625 \div 125}{1000 \div 125} = \frac{5}{8} \] So, 0.625 as a fraction in its lowest terms is \(\frac{5}{8}\).

To convert the decimal `0.625` to a fraction in its lowest terms, we can follow these steps: 1. Express the decimal as a fraction with a denominator that is a power of 10. 2. Simplify the fraction by finding the greatest common divisor (GCD) and dividing both the numerator and the denominator by this GCD. Here's how you can implement this in C#: ```csharp using System; public class DecimalToFractionConverter { public static void Main() { double decimalValue = 0.625; Fraction fraction = ConvertToFraction(decimalValue); Console.WriteLine($"{decimalValue} as a fraction is {fraction.Numerator}/{fraction.Denominator}"); } public static Fraction ConvertToFraction(double value) { // Find the numerator and denominator int numerator = (int)(value * 1000); // Since 0.625 has three decimal places int denominator = 1000; // Simplify the fraction by finding the GCD int gcd = GreatestCommonDivisor(numerator, denominator); return new Fraction(numerator / gcd, denominator / gcd); } private static int GreatestCommonDivisor(int a, int b) { while (b != 0) { int temp = b; b = a % b; a = temp; } return a; } } public struct Fraction { public int Numerator { get; } public int Denominator { get; } public Fraction(int numerator, int denominator) { if (denominator == 0) throw new ArgumentException("Denominator cannot be zero."); this.Numerator = numerator; this.Denominator = denominator; } public override string ToString() { return $"{Numerator}/{Denominator}"; } } ``` ### Explanation: 1. **ConvertToFraction Method**: - The method takes a `double` value and converts it to a fraction. - It multiplies the decimal by 1000 (since there are three decimal places in 0.625) and sets the denominator to 1000. - It then finds the greatest common divisor (GCD) of the numerator and denominator using the `GreatestCommonDivisor` method. - Finally, it returns a new `Fraction` object with the simplified numerator and denominator. 2. **GreatestCommonDivisor Method**: - This method uses the Euclidean algorithm to find the GCD of two integers. 3. **Fraction Struct**: - This struct represents a fraction with properties for the numerator and denominator. - It includes a constructor to initialize the fraction and an override of the `ToString` method to provide a readable string representation. This implementation ensures that the decimal is accurately converted to a fraction in its lowest terms.