To convert a decimal into a fraction, begin by expressing the decimal as a fraction with a denominator of $10$, $100$, or another power of $10$, and then simplify the fraction.

To illustrate, let’s take the decimal $0.75$. This can be represented as the fraction $\frac{75}{100}$, because $0.75$ signifies $75$ hundredths. The number of decimal places indicates the appropriate denominator: one decimal place corresponds to tenths ($10$), two decimal places correspond to hundredths ($100$), and so forth.

Once you have expressed the decimal as a fraction, the next step is to simplify it. Simplification involves finding the greatest common divisor (GCD) of the numerator and the denominator, and then dividing both by that number. For the fraction $\frac{75}{100}$, the GCD is $25$. Therefore, we divide both the numerator and the denominator by $25$:

This means that $\frac{75}{100}$ simplifies to $\frac{3}{4}$. Consequently, the decimal $0.75$ can be expressed as the fraction $\frac{3}{4}$.

For repeating decimals, such as $0.333...$, you can utilize algebra to convert them. Let $x = 0.333...$. Then, multiplying both sides by $10$ gives $10x = 3.333...$. By subtracting the first equation from the second, we have:

This simplifies to:

Solving for $x$ gives:

which simplifies to:

By following these steps, you can effectively convert any decimal into a fraction and reduce it to its simplest form.