Round #624

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# using the `System.Numerics` namespace, which provides a `Fraction` class for handling rational numbers: ```csharp using System; using System.Numerics; class Program { static void Main() { double decimalValue = 0.625; Fraction fraction = new Fraction(decimalValue); Console.WriteLine($"The fraction in lowest terms is: {fraction}"); } } ``` ### Explanation: 1. **Using `System.Numerics.Fraction`**: - The `Fraction` class from the `System.Numerics` namespace automatically handles the conversion of a decimal to its simplest fractional form. - When you create a new `Fraction` object with a decimal value, it internally calculates the numerator and denominator in their lowest terms. 2. **Output**: - The program will output the fraction `5/8`, which is the simplest form of `0.625`. ### Additional Notes: - If you need to implement this manually without using the `Fraction` class, you can follow these steps: - Multiply the decimal by a power of 10 to get an integer. - Find the GCD of the numerator and the denominator. - Divide both the numerator and the denominator by their GCD. Here's a manual implementation: ```csharp using System; class Program { static void Main() { double decimalValue = 0.625; // Convert decimal to fraction int numerator = (int)(decimalValue * 1000); // Multiply by 1000 to get an integer int denominator = 1000; // Denominator is 1000 since we multiplied by 1000 // Simplify the fraction int gcd = GCD(numerator, denominator); numerator /= gcd; denominator /= gcd; Console.WriteLine($"The fraction in lowest terms is: {numerator}/{denominator}"); } static int GCD(int a, int b) { while (b != 0) { int temp = b; b = a % b; a = temp; } return a; } } ``` ### Explanation of Manual Implementation: 1. **Multiplication by Power of 10**: - `numerator = (int)(decimalValue * 1000);` converts the decimal to an integer by multiplying it by 1000. 2. **Finding GCD**: - The `GCD` method uses the Euclidean algorithm to find the greatest common divisor of the numerator and denominator. 3. **Simplifying the Fraction**: - Both the numerator and denominator are divided by their GCD to get the fraction in its lowest terms. This manual approach gives you more control over the process, but using `System.Numerics.Fraction` is generally simpler and less error-prone for most practical purposes.