Question

What is 2.4 as a fraction?

Answer 1

Hint: We have to convert the given number (which is given in decimal format) to a fraction. To obtain a mixed fraction, basically, first we will split the given number into i.e. that are the integer portion and the decimal portion. The integer portion will be kept as it is and we will convert the decimal part into a fraction, and for the simple fraction, we will simplify that mixed fraction.

Complete step by step solution:
In the question, the value we are given to be solved is "2.4"
Let's split the number into an integer part and decimal part
\[2.4=2+0.4\]
Now we will keep the integer part (that is 2) as it is, and we will work on the decimal part to convert it into the fractional part,
\[0.4=\dfrac{4}{10}\]
Let us see how did we put a 10 here,
Just locate the decimal point, now count the total digits after the decimal, let's say there are n digits after decimal so we will remove the decimal and put a \[{{10}^{n}}\] in the denominator.
Let’s say for example we have 3 digits after the decimal point then we will put \[{{10}^{3}}\] that is 1000 in the denominator. Here we were having \[0.4\] that is one point after the decimal point so we did give a \[{{10}^{1}}\] that is 10 in the denominator.
So, what is our final expression now,
\[2.4=2+\dfrac{4}{10}.....................(i)\]
By convention how do we write this in mixed fraction, just simply hiding the plus sign, so this value in mixed fraction looks something like this,
\[2.4=2\dfrac{4}{10}\]
We also want the value in simple fraction so just solving equation \[(i)\]
\[\begin{align}
  & \Rightarrow 2.4=\dfrac{(2\times 10)+4}{10} \\
 & \Rightarrow 2.4=\dfrac{20+4}{10} \\
 & \Rightarrow 2.4=\dfrac{24}{10} \\
\end{align}\]
We can further simplify it because the denominator and the numerator are having a common factor that is \[2\]. So, the given value in simple fraction become,
\[2.4=\dfrac{12}{5}\]

Note: To convert it into a simple fraction we need not split it into two parts, note that in \[2.4\] we have one digit after the decimal so we can just simply write it \[\dfrac{24}{10}\] and further \[\dfrac{12}{5}\]. You can simplify the equation \[(i)\]using this formula \[a+\dfrac{b}{c}=\dfrac{ac+b}{c}\] or by simply taking LCM and then solving it.