Question

Which choice shows the answer to the following mathematical operation with the correct number of significant figures
$2.8 \times 8.96 = ?$
$\left( A \right)25.09$
$\left( B \right)25.1$
$\left( C \right)25$
$\left( D \right)25.08$
$\left( E \right)25.088$

Answer 1

Hint : Significant figures are those numbers which contribute towards the calculation . We have rules for counting significant figures . By following those rules we can easily get the required answer . first multiply the above number and then apply the rules .

Complete Step By Step Answer:
Rules of significant figures :
$\left( 1 \right)$ Non zero digits are considered significant
$\left( 2 \right)$ Any zero between two significant figures are always significant
$\left( 3 \right)$ A final zero in the decimal portion is only significant . like $.500$ here zeros are significant means we are having three significant figures . but , $.006$ here the zeros are not significant so here only one significant figure is present .
In case of multiplication : the answer when reported must be of least precise number . We need to check the number of significant figures present in the operational numbers and also the decimal places. The number with least precise significant figures then we have to get our answer accordingly.
After multiplying the equation we get :
$2.8 \times 8.96 = 25.088$
By following the above rule we can say we have 4 significant figures in the number present . But the number $2.8$ has two significant figures and $8.96$ have three significant figures so our answer will be two significant figures as two significant figures is less precise than three . So our answer will be $25.1$ hence option $\left( B \right)$ .

Note :
The exact number is a term we use when we have to count the exact something is present . like there are $100$ chairs , here we it does not affect the accuracy it is showing the exact number of chairs is present .
In case of addition and subtraction : In this do the subtraction and addition in a general rule . Then round your answer according to the least precise number in the problem .