Question

What is 2.4 as a percent and as a fraction or mixed number?

Answer 1

Hint: Given is a decimal number. We are asked to express this number in the form of percent and fraction or mixed number. Now first we will convert it into percent by multiplying it by 100. Then it comes to express it as a fraction or as they mentioned mixed numbers. For that we will remove the decimal and express it in simplest form.

Complete step-by-step answer:
I.Given that,
2.4 is the number given.
Percent form:
In order to write in this form we just know that the number is to be multiplied by 100 and it can be written as percent.
So we can write this as,
\[
   = 2.4 \times 100 \\
   = 240\% \;
\]
This shows that it is 240%.

II.Fraction form:
Now we will remove the decimal from the fraction above, by multiplying the numerator and denominator by 10
\[ = \dfrac{{2.4 \times 10}}{{10}}\]
On multiplying,
\[ = \dfrac{{24}}{{10}}\]
Now to write this in simplest form we will need to find the HCF of numerator and denominator.
Factors of 24 are 1,2,3,4,6,8,12,24.
Factors of 10 are 1,2,5,10.
Now the common factors are 1,2.
And thus the HCF is 2. Now divide the N and D by 2 we get,
\[ = \dfrac{{12}}{5}\]
Thus this is the fraction form. And if we observe that this is the improper fraction form. So we can write it in mixed fraction form by dividing the numerator by the number in the denominator. So on dividing 12 by 5 we get 2 as remainder.
As we know mixed fraction is written as, \[quotient\dfrac{{remainder}}{{divisor}}\]
So the number will be, \[\dfrac{{12}}{5} = 2\dfrac{2}{5}\]

Note: Note that we have expressed this fraction as a mixed number because the fraction is an improper fraction such that the denominator is smaller than the numerator. So we can express this in mixed fraction form. Also note that here coincidently the quotient and remainder are same so don’t get confused. But in any other case you should write them in their respective places.