Question

Solve with due regard to significant figures: $\dfrac{{5.42 \times 0.6753}}{{0.085}}$

Answer 1

Hint: When the problem is related to multiplication or division, we need to first solve the problem as usual and need to look at the significant figures for each number given in the problem. Then, we need to find the least number of significant figures. Then we need to correct the final answer to the least number of significant figures.

Complete step-by-step answer:
First, we shall learn the rules to find the significant figures.
$\bullet$ We need to consider every non-zero digit as a significant figure.
For example, $12$ contains two significant figures
$\bullet$ We need to consider zero in between the numbers as significant figures.
For example, $103$ contains three significant figures.
$\bullet$ We should not consider zeroes at the end of the answer when the decimal point is not used as significant figures.
For example, $100$ contains only one significant figure.
$\bullet$ We should consider zeroes at the end of the answer when the decimal point is used as significant figures. (i.e. we need to consider final zeros in the fractional part)
For example, $1.60$ contains three significant figures.
Now, we shall get into the given problem.
We need to solve $\dfrac{{5.42 \times 0.6753}}{{0.085}}$
$\dfrac{{5.42 \times 0.6753}}{{0.085}}$$ = \dfrac{{3.66}}{{0.085}}$
$ = 43.06$
Thus, we have $\dfrac{{5.42 \times 0.6753}}{{0.085}}$$ = 43.06$
Now, we need to find the significant figures for each number.
a) Let us consider $5.42$
Here the number consists of non-zero digits. So, $5.42$contains three significant digits.
b) Let us consider $0.6753$
Here we need to consider fractional parts alone and no need to consider the zero before the decimal point. Hence $0.6753$contains four significant digits.
c) Let us consider $0.085$
Here we don’t need to consider the zero before and after the decimal point. Thus, $0.085$contains two significant figures.
Thus, the least significant digit is two.
We need to correct the obtained answer to the least significant digit.
_{We have found}$\dfrac{{5.42 \times 0.6753}}{{0.085}}$$ = 43.06$
Therefore, $\dfrac{{5.42 \times 0.6753}}{{0.085}}$$ = 43$
(Here $43$ contain two significant digits)

Note: It is to be noted that the above rules are applicable only for multiplication and division.
We shall consider $45.63 + 2.6$
We know that $45.63 + 2.6 = 48.23$
When we need to find the answer regarding significant figures, we need to find the least number of places in the decimal portion.
Thus, $45.63$ contains two places and $2.6$ contains one place in the decimal portion.
So, one is the obtained least place and we need to round off the obtained answer to that least place.
Hence, we have $45.63 + 2.6 = 48.2$ and we have rounded the answer to the least decimal places.