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To convert a decimal to a fraction, you need to follow a few simple steps. First, understand the given decimal. For example, let's consider the decimal 0.464. The overall goal is to write this decimal as a fraction where the numerator is derived from the digits of the decimal, and the denominator is a power of 10 depending on the number of decimal places.
Imagine the decimal number 0.464. Here, it has three decimal places, so you place the number 464 over 1000 (since 1000 has three zeros, corresponding to the three decimal places). Therefore, 0.464 becomes \(\frac{464}{1000}\).
This fraction clearly states the value of the original decimal in fractional form.

Once you've converted the decimal to a fraction, the next step is to simplify it as much as possible. Simplifying a fraction means reducing it to its simplest form where the numerator and the denominator share no common factors other than 1.
Take our example \(\frac{464}{1000}\). This fraction can be simplified to make it easier to understand or work with. To simplify, you'll need to divide both the numerator and the denominator by the greatest common divisor (GCD) of 464 and 1000.
Simplifying fractions is very helpful for making calculations easier and presentation cleaner. In this case: \(\frac{464}{1000}\) simplifies to \(\frac{58}{125}\).

Finding the greatest common divisor (GCD) is crucial for simplifying fractions. The GCD is the largest number that can evenly divide both the numerator and the denominator.
Let's take our fraction \(\frac{464}{1000}\). To find the GCD of 464 and 1000, list out the factors of each number. The factors of 464 are: 1, 2, 4, 8, 16, 29, 58, 116, 232, and 464. The factors of 1000 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.
The common factors are 1, 2, 4, and 8. The largest, of course, is 8, which is the GCD.
Use the GCD to simplify the fraction by dividing both the numerator and the denominator by 8: \(\frac{464 \div 8}{1000 \div 8} = \frac{58}{125}\). Now, you have the fraction in its simplest form.