Question

The respective number of significant figures for the numbers \[23.023,0.0003\] and \[2.1\times {{10}^{-3}}\] are:
\[A)5,1,2\]
\[B)5,1,5\]
\[C)5,5,2\]
\[D)4,4,2\]

Answer 1

Hint: Significant figures in a particular number refer to the necessary numbers, required to represent that number accurately. To count the number of significant figures in a number, we have a certain set of rules. Going through these rules, we can easily count the number of significant figures in the given numbers.

Complete answer:
Significant figures in a particular number refer to the necessary numbers, required to represent that number accurately. To count the number of significant figures in a number, we have a certain set of rules, as given below:
- All non-zero figures are significant
- All zeroes between two non-zero figures are significant
- Leading zeroes (before non-zero figures) are not significant
- Trailing zeroes (after non zero figures) on right side of decimal are significant
- Trailing zeroes (after non zero figures) on the left side of decimal are significant. However, in case of a non-decimal number, trailing numbers (after non zero figures) are not significant
Now, let us count the number of significant figures in the given numbers using these rules.
\[a)23.023\]
According to the rule, ‘All zeroes between two non-zero figures are significant’, all the given figures in the number are significant and hence, the total number of significant numbers is $5$.

\[b)0.0003\]
According to the rule, ‘Leading zeroes (before non-zero figures) are not significant’, all the numbers except $3$ are not significant and hence, the number of significant figures is $1.$

\[c)2.1\times {{10}^{-3}}\]
The number can be written as $0.0021$. According to the rule, ‘Leading zeroes (before non-zero figures) are not significant’, all the numbers except $2$ and $1$ are not significant and hence, the number of significant figures is $2$.

Therefore, from the above explanation, it is clear that the correct answer is option $A$.

Note:
All the given rules for significant and non-significant figures need to be remembered to solve such questions. The fifth/last rule stated in the above set of rules needs to be clearly differentiated since this rule is tricky and can always be a reason for confusion.