Question

Express $12\dfrac{8}{3}$ as a decimal?
A. $14.6667$
B. $13.333$
C. $14.25$
D. $13.98$

Answer 1

Hint:Though this problem is straightforward, one trick to solve such sums is by converting mixed fraction to normal form and then to nearest $10s$. By doing this the student will not have to sit and divide the numerator and the denominator. Chances of going wrong are also very less. The first step is to find the nearest $10s$ for $3$. After that, the student has to multiply the numerator and denominator by the same number so that the denominator has $10$ or it’s multiple. After this step, the student will just have to input the decimal point to get the final answer. In this fraction we can see that $3$ is an odd number, so we will have to convert the fraction such that the denominator has $30$.

Complete step by step solution:
The first step is to convert the mixed fraction to normal form,
$12\dfrac{8}{3} = \dfrac{{44}}{3}$
The second step is to convert the denominator to $30$.
Multiplying by $100$ to both numerator and denominator, we get
$\dfrac{{44}}{3} = \dfrac{{44}}{3} \times \dfrac{{10}}{{10}}.............(1)$
$\dfrac{{44}}{3} = \dfrac{{440}}{{30}} = ............(2)$
Now we should ignore the denominator which has $10$, considering the fraction as $\dfrac{{440}}{3}$. We will now have to divide the fraction.
Thus the new form of the fraction would be approximately
$\dfrac{{440}}{3} \times (\dfrac{1}{{10}}) = 146.666 \times (\dfrac{1}{{10}})......(3)$
Ignoring the digits after the decimal point since we have to divide it by $10$, further.
From equation $3$ we can say that the decimal value for $\dfrac{{44}}{3}$ is $14.6667$.

Answer to this question is option A.$14.6667$.

Note: This numerical is very simple if it is done by this method. Otherwise in the case of a complex numerical for example $\dfrac{{3343}}{{800}}$, if the student sits and divides the numerator and denominator, he may consume a lot of time. On the contrary, just multiplying the numerator and denominator by a common multiple would solve the sum faster. Thus the students are always advised to bring the denominator in terms of its nearest $10th$ or $100th$ multiple and divide the number if it is an odd number like the above numerical and finally then convert the number to decimal. Also, the chances of making errors by following this method are less compared to direct division.