$0.125$ to fraction

Convert $0.125$ to a fraction.

Recall that every mixed number consists of an integer part and a proper fraction. Also, a decimal consists of an integer and a decimal parts.

Mixed numbers and decimals are very similar: if they represent the same number, their integer parts are equal, and what we want is to convert the decimal part of the decimal into the fractional part of the mixed number.

Our decimal consists of the integer part $0$ and the decimal part $0.125$.

So, we ignore the integer part (in our case, integer part equals $0$, so there is nothing to ignore) and work with the decimal part $0.125$.

Recall that every number can be represented as a fraction with a denominator that equals $1$.

In our case, we can write that $0.125 = \frac{0.125}{1}$.

Since the decimal part contains $3$ digits (to the right of the decimal point), we need to multiply our number by $10^{3} = 1000$ to obtain an integer.

Now, using the equivalence of fractions, we can write that $\frac{0.125}{1} = \frac{0.125\cdot {\color{red}1000}}{1\cdot {\color{red}1000}} = \frac{125}{1000}$.

Next, try to reduce the fraction.

Since the greatest common divisor of the numerator and the denominator equals $125$, we can write that $\frac{125}{1000} = \frac{1\cdot {\color{red}125}}{8\cdot {\color{red}125}}$.

And don't forget about the integer part.

Since the integer part equals $0$, we don't add anything. This means that we won't get a mixed number, just a proper fraction.

$0.125 = \frac{1}{8}$A