Question

Convert the following decimal number into fraction in the simplest form.

$13.964$

Answer 1

Converting $13.964$ into a fraction in the simplest form:

Since there are three digits after a decimal point, so put $3$ zeroes after $1$ in the denominator.

Therefore $13.964=\frac{13964}{1000}$

Prime factors of $13964$ and $1000$ are

$$\begin{gathered} 13964=2\times 2\times 3491 \\ 1000=2\times 2\times 2\times 5\times 5\times 5 \end{gathered}$$

The highest common factor of $13964$ and $1000$ is $2\times 2=4$.

Therefore dividing by the common factor $4$ to reduce it into the simplest form, we get

$\frac{13964÷4}{1000÷4}=\frac{3491}{250}$

Therefore, $13.964=\frac{3491}{250}$