What is .125 as a fraction and what is it in simplified form?

To convert a decimal into a fraction, divide the numbers after the decimal point by 10 to the power of the quantity of numbers after the decimal.

The decimal number 0.125 has the number 125 after the decimal point, and since there are 3 numbers after the decimal, 10 to the power of 3 gives 1,000.

Therefore, your decimal in fractional form would initially look like this:

$$ \frac{125}{1000} $$

This is the decimal $0.125$ in its initial fractional form — but it’s not in its simplest form yet.

How To Reduce A Fraction

Reducing a fraction means dividing both the numerator and the denominator by a common factor. This makes both numbers smaller, without changing the value of the fraction.

To reduce our fraction:

A) Divide both 125 and 1000 by 5:

$$ \begin{array} \frac{125 \div 5}{1000 \div 5} & & \text{divide by $5$} \ \frac{25}{200} \end{array} $$

B) Again, divide both numbers by 5:

$$ \begin{array} \frac{25 \div 5}{200 \div 5} & & \text{divide by $5$} \ \frac{5}{40} \end{array} $$

C) Again, divide both numbers by 5:

$$ \begin{array} \frac{5 \div 5}{40 \div 5} & & \text{divide by $5$} \ \frac{1}{8} \end{array} $$

As you can no longer divide both numbers by a common factor, this is the simplest form of the fraction representing $0.125$.

Reducing Using the Highest Common Factor

You can also simplify a fraction in one step if you know the highest common factor (HCF) of the numerator and denominator.

Let’s find the HCF of 125 and 1000:

$$ 125 = {1, 5, 25, 125} \ 1000 = {1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 125, 200, 250, 500, 1000} $$

The shared common factors are ${1, 5, 25, 125}$, and the highest is $125$.

So reduce the fraction in one go:

$$ \begin{array} \frac{125 \div 125}{1000 \div 125} & & \text{divide by HCF $125$} \ \frac{1}{8} \end{array} $$

Same result — just fewer steps.

Summary

The decimal number $.125$ can be expressed as the fraction $\frac{1}{8}$.

To convert a decimal to a fraction, count how many digits are after the decimal point, use that to form your initial denominator (a power of ten), then reduce both numbers by a common factor — ideally the highest common factor — to get the simplest form.

Next, you might want to try working out what .375 as a fraction or .625 as a fraction would be.