Question

What is \[5\dfrac{1}{8}\] as a decimal?

Answer 1

Hint: We are given a mixed fraction and we have to convert this mixed fraction to a decimal. We will begin our conversion by first converting the given mixed fraction into either a proper fraction or an improper fraction. In our case, we will get an improper fraction, which is, \[\dfrac{41}{8}\]. Now, we have the fraction, we will now proceed by dividing the numerator by denominator, that is, we will be dividing 41 by 8 and we will get the decimal form as the quotient. Hence, we will get the decimal equivalent of the given mixed fraction.

Complete step by step answer:
According to the given question, we are given a mixed fraction and we are asked to find the decimal equivalent of it.
The given mixed fraction we have is,
\[5\dfrac{1}{8}\]----(1)
We will begin our conversion by first converting the given mixed fraction to either a proper fraction or an improper fraction.
So, we will multiply the denominator 8 by 5 and then add 1 to it and the result becomes the numerator, we get,
\[\Rightarrow \dfrac{41}{8}\]----(2)
In our case, we have got an improper fraction. We will further continue by using the long division method, that is, we will divide the numerator by the denominator.
We will now divide the numerator 41 by the denominator 8 as per equation (2), so we have,
\[8\overset{5.125}{\overline{\left){\begin{align}
  & 41 \\
 & \underline{-40} \\
 & 10 \\
 & \underline{-8} \\
 & 20 \\
 & \underline{-16} \\
 & 40 \\
 & \underline{-40} \\
 & \_0\_ \\
\end{align}}\right.}}\]
So, we get the quotient as \[5.125\] and it is in the decimal form.

Therefore, the decimal form of the given mixed fraction \[5\dfrac{1}{8}=5.125\].

Note: While converting the mixed fraction into an improper fraction, the numbers should be multiplied correctly. Also, the long division if used should be done in a clear and concise manner. When using the long division method, the decimal form is always obtained as the quotient and not the remainder.