Question

Calculate the value of the expression by appropriate rounding off of the numbers$3.72 \div 0.02$

Answer 1

Hint:We will see two approaches to find the solution to this question. While the first approach revolves around first rounding off the dividend 3.72 and then performing the division, the second approach involves carrying out the division first followed by the rounding off of the quotient to the highest decimal place.

Complete step-by-step Solution:
Now, we have to find the value of $3.72 \div 0.02$ by dividing$3.72\,\,by\,\,0.02$.
Now, for the number $3.72$, to be rounded off to the highest decimal place which is units’ place in this case, the digit in the hundredth place is to be considered and rounded off to the tenth place. So the digit in the hundredth place is $2$ which is less than or equal to $5$, the number will be rounded off to the same place in the tenth place. So $3.72$will become $3.70$, now again rounding off to the nearest units’ place we will look at the digit at tenth place, which is $7$. Now $7$ being greater than $5$ will mean that the $3$ in units’ place will increase by$1$.
That is, it will become
$3 + 1 = 4$
So the number $3.72$ when rounded off to the highest decimal place will become:
$3.72 \approx 4.00$
So now we need to find the value of $4.00 \div 0.02$
So dividing$4.00\,\,by\,\,0.02$we will get
$
   = \dfrac{{4.00}}{{0.02}} \\
   = \dfrac{{4.00}}{{\dfrac{2}{{100}}}} \\
   = \dfrac{{400}}{2} \\
   = 200 \\
 $
So, the final answer we get on rounding off $3.72$to the nearest $1s$ place as $4.00$and dividing by$0.02\,\,is\,\,200$.

Alternate approach:
The other way to go about dividing $3.72\,\,by\,\,0.02$will be to first divide $3.72\,\,by\,\,0.02$and the round off the answer thus obtained.
So on dividing $3.72\,\,by\,\,0.02$we will get
$
    =\dfrac{{3.72}}{{0.02}} \\
   = \dfrac{{\dfrac{{372}}{{100}}}}{{\dfrac{2}{{100}}}} \\
   = \dfrac{{372}}{2} \\
   = 186 \\
 $
Now we will round off $186$ to the nearest $100s$ place.
To round off to the nearest $100s$ place we will first check the digit at $10s$ place. If the digit is greater than or equal to $5$ then the number in the $100s$ place will increase by $1$.
In $186$ the digit in the $10s$ place is $8$, which is greater than $5$, so the number in $100s$ place being $1$ will increase by $1$ and become $2$ while the digits at tens’ place and units’ place will become 0 respectively.
So $186$ when rounded off to the nearest $100s$ will become $200$.
Therefore, the answer on rounding off will stay the same irrespective of the approach.
Hence, $3.72 \div 0.02$ will give us the quotient as $200$, when rounded off properly to the highest decimal place.

Note:While rounding off it is the dividend that is being rounded off because the divisor already has only $1$ significant digit so it cannot be further rounded off to $2$, since $2$ being smaller than $5$, will otherwise make the denominator $0$ and the division will become invalid, since anything divided by $0$ is not defined.