Question

How do you convert $9\dfrac{1}{2}$ into a decimal and percent?

Answer 1

Hint: First of all convert the given mixed fraction into the improper fraction using the relation: $a\dfrac{b}{c}=\dfrac{ac+b}{c}$. Now, to convert this 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 ${{10}^{n}}$. Now, multiply this decimal number obtained with 100 to get the required percentage.

Complete step by step answer:
Here, we have been provided with a mixed fraction $9\dfrac{1}{2}$ and we are asked to convert it into a decimal and percent. But first we need to convert the mixed fraction into the improper fraction.
Now, if we have to convert any mixed fraction of the form $a\dfrac{b}{c}$ into an improper fraction then we use the relation: $a\dfrac{b}{c}=\dfrac{ac+b}{c}$. So, we have,
\[\begin{align}
  & \Rightarrow 9\dfrac{1}{2}=\dfrac{\left( 9\times 2 \right)+1}{2} \\
 & \Rightarrow 9\dfrac{1}{2}=\dfrac{18+1}{2} \\
 & \Rightarrow 9\dfrac{1}{2}=\dfrac{19}{2} \\
\end{align}\]
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 in the denominator so multiplying it with 5 we can get the denominator equal to 10. To balance the expression we have to multiply the numerator also with the same number, so we get,
\[\begin{align}
  & \Rightarrow \dfrac{19}{2}=\dfrac{19\times 5}{2\times 5} \\
 & \Rightarrow \dfrac{19}{2}=\dfrac{95}{10} \\
 & \Rightarrow \dfrac{19}{2}=9.5 \\
\end{align}\]
Therefore, the decimal representation of $9\dfrac{1}{2}$ is 9.5.
Now, to convert any decimal number into a percent we multiply the decimal number with 100, so multiplying 9.5 with 100, we get,
$\Rightarrow 9.5\times 100=950$
Therefore, $9\dfrac{1}{2}$ is represented as 950% in the percentage form.

Note:
One must remember how to convert a fraction into a decimal number. Now, it may be given to us a number in percentage form and we would be asked to write it as a fraction or decimal. In such cases we will follow the reverse process and divide the given percentage with 100 to get the answer. Remember the basic definition of ‘percentage’.