Question

How do you convert \[3\dfrac{3}{8}\] to a decimal and a percentage?

Answer 1

Hint: In the given question, we have been asked to convert a fraction into a decimal as well as a percent. First, we are going to convert the fraction into a decimal by dividing the numerator by the denominator and calculating the result. Then we convert the fraction into a percent by multiplying it by \[100\].

Complete step by step answer:
The given number is \[3\dfrac{3}{8} = 3 + \dfrac{3}{8}\].
First, we convert it to decimal by solving \[\dfrac{3}{8}\] and then adding \[3\] to it,
\[8\mathop{\left){\vphantom{1\begin{array}{l}{\rm{ }}3\\\dfrac{{{\rm{ }} - 0}}{{{\rm{ }}30}}\\\dfrac{{{\rm{ }} - 24}}{\begin{array}{l}{\rm{ }}60\\{\rm{ }}\dfrac{{{\rm{ }} - 56}}{\begin{array}{l}{\rm{ }}40\\{\rm{ }}\dfrac{{{\rm{ }} - 40}}{0}\end{array}}\end{array}}\end{array}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{array}{l}{\rm{ }}3\\\dfrac{{{\rm{ }} - 0}}{{{\rm{ }}30}}\\\dfrac{{{\rm{ }} - 24}}{\begin{array}{l}{\rm{ }}60\\{\rm{ }}\dfrac{{{\rm{ }} - 56}}{\begin{array}{l}{\rm{ }}40\\{\rm{ }}\dfrac{{{\rm{ }} - 40}}{0}\end{array}}\end{array}}\end{array}}}}
\limits^{\displaystyle\,\,\, {0.375}}\]
So, \[\dfrac{3}{8} = 0.375\]
Hence, \[3\dfrac{3}{8} = 3 + 0.375 = 3.375\]
Now, we convert the number to percent by multiplying it by \[100\],
\[\dfrac{{27}}{8} \times 100 = \dfrac{{2700}}{8} = \dfrac{{675}}{2} = 337\dfrac{1}{2}\% \]

So, \[3\dfrac{3}{8} = 337\dfrac{1}{2}\% \]

Additional Information:
We can easily convert a given number into percent by applying the above-mentioned formula. But, if we have to do the reverse – convert the percent to number, we simply divide the percent by 100. Then, we reduce the derived number to the lowest term and that is going to give us the answer.


Note: For solving the fraction into a decimal, we just divide the numerator by the denominator. But, if we have to calculate the reverse – convert a decimal to fraction, we first count the number of digits after the decimal point; let it be ‘c’. Then we take the complete number without the decimal point as the numerator and take the denominator equal to \[1\] followed by \[c\] zeroes.