Question

How many significant figures should be present in the answer of the following calculations?
(i).\[\dfrac{{0.02856 \times 298.15 \times 0.112}}{{0.5785}}\]
(ii).\[5 \times 5.364\]
(iii).\[0.0125 + 0.7864 + 0.0215\]

Answer 1

Hint: The number of significant figures /digits present in the solution depends on the term of the question having the least number of significant figures. And the exact numbers are not counted in the significant figures.
Step by step solution: to solve this question. First we need to understand the significant figures and the major rules that govern them.
So basically, Significant figures are the digits of a number that are meaningful in terms of accuracy and precision.
Let’s recall five major rules governing the significant figures.
All the non-zero digits are significant
Leading zeroes are not significant
Zeroes between two non-zero digits are significant
Zeroes to the right of the decimal is significant
Zeroes to the right of the non-zero digit without the decimal is not significant
Now, in the first option, the least number of precise terms is \[0.112\] having \[3\] significant figures. So the solution of \[option(i)\]will also have \[3\] significant figures.
In\[option(ii)\], the least precise term in the question is \[5.364\] having \[4\] significant figures. Thus, the solution of this equation will have \[4\] significant figures. Here we have not considered \[5\] because it is an exact number and exact numbers have an infinite number of significant figures.
In\[option(iii)\], we can see, by the rules, that the least number of significant figures are up to \[4\] decimal places. So, the solution of the given equation will have \[4\]significant figures.

Note:
While dealing with the scientific notations like \[N \times {10^y}\], as we learned all the rules above, we can say the \[N\]number of digits are significant and \[10\] and \[power{\text{ y}}\] are not significant because \[10\] is an exact figure.