Question

How do you convert the number \[\dfrac{11}{4}\] from fraction form to decimal form?

Answer 1

Hint: We start solving the problem by equating the given number to a variable. We then write the numerator of the given fraction as the sum of two numbers 8 and 3 to proceed through the problem. We then make use of the fact that $\dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}$ to proceed further through the problem. We then make the necessary calculations to get the required fraction form of the given number.

Complete step by step answer:
According to the problem, we are asked to convert the given number \[\dfrac{11}{4}\] from fraction form to decimal form.
Let us assume $f=\dfrac{11}{4}$ ---(1).
We know that $11=8+3$. Let us substitute this result in equation (1).
$\Rightarrow f=\dfrac{8+3}{4}$ ---(2).
We know that $\dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}$. Let us use this result in equation (2).
$\Rightarrow f=\dfrac{8}{4}+\dfrac{3}{4}$.
$\Rightarrow f=2+0.75$.
$\Rightarrow f=2.75$.

So, we have found the decimal form of the given number \[\dfrac{11}{4}\] as 2.75.
$\therefore $ The conversion of the number \[\dfrac{11}{4}\] from fraction form to decimal form is 2.75

Note: Whenever we get this type of problem, we try to write the numerator as a sum of two numbers in which one number is multiple of the denominator. We can also solve the given problem by performing long division by taking 11 as dividend and 4 as divisor to get the required answer. Similarly, we can expect problems to find the quotient and remainder when 25 is divided by 7.