Question

How do you convert $\dfrac{892}{16}$ to a decimal?

Answer 1

Hint: Write the numbers in the numerator and the denominator as the product of its prime factors and cancel the common factors if present. Now, to convert the simplified fraction into the decimal try to make the denominator equal to 10 or of the form ${{10}^{n}}$ where n will be any integer. Move the decimal point to the left side according to the number of zeroes in ${{10}^{n}}$.

Complete step by step answer:
Here, we have been provided with an improper fraction $\dfrac{892}{16}$ and we are asked to convert it into a decimal. But first we need to simplify the fraction by cancelling the common factors.
Now, to check if there are any common factors of the numerator and the denominator we need to write them as the product of their prime factors, so we get,
$\Rightarrow \dfrac{892}{16}=\dfrac{2\times 2\times 223}{2\times 2\times 2\times 2}$
Cancelling the common factors and simplifying the fraction, we get,
$\begin{align}
  & \Rightarrow \dfrac{892}{16}=\dfrac{223}{2\times 2} \\
 & \Rightarrow \dfrac{892}{16}=\dfrac{223}{{{2}^{2}}} \\
\end{align}$
Now, to convert this improper fraction into the decimal we need to make the denominator equal to 10 or of the form ${{10}^{n}}$ where n will be any integer. Clearly, we can see that we have ${{2}^{2}}$ in the denominator so multiplying it with ${{5}^{2}}$ we will get the denominator equal to ${{10}^{2}}$. To balance the expression we have to multiply the numerator also with the same number, so we get,
\[\begin{align}
  & \Rightarrow \dfrac{223}{{{2}^{2}}}=\dfrac{223\times {{5}^{2}}}{{{2}^{2}}\times {{5}^{2}}} \\
 & \Rightarrow \dfrac{223}{{{2}^{2}}}=\dfrac{223\times 25}{{{10}^{2}}} \\
 & \Rightarrow \dfrac{223}{{{2}^{2}}}=\dfrac{5575}{100} \\
\end{align}\]
So, we have two zeroes in the denominator therefore we need to move 2 places towards the left side to mark the decimal point, so we get,
\[\Rightarrow \dfrac{223}{{{2}^{2}}}=55.75\]
Therefore, the decimal representation of $\dfrac{892}{16}$ is 55.75.

Note:
One must remember how to convert a fraction into a decimal number. You may see that here we are getting a terminating decimal number. This is because here the denominator of the initial fraction is of the form ${{2}^{n}}$. In general remember that we will obtain a terminating decimal only when we have the denominator of the form ${{2}^{n}}$ or ${{5}^{n}}$. In all other cases we will get non – terminating repeating decimal numbers.