Question

The number of significant figures in \[6.02 \times {10^{23}}\] is :
A. 23
B. 3
C. 4
D. 26

Answer 1

Hint: Significant figures in any expression or numeral or decimal are just the number of significant digits from 0-9. When a number is expressed in scientific notation, the expressions in which all the zeros to the right-hand side of the decimal point are significant.

Complete Step by Step Solution:
Whether a number is significant or not is governed by some rules. One of the rules states that non-zero numbers are significant.
If we consider the number 55.78, there is a count of four significant figures.
Another rule states that if zeroes are there between any no.of significant numbers then the zeroes have significance.
So, for the given question, 6.02 has a total of four significant digits as the zero between six and two is also considered a significant number.
When numbers are expressed in scientific notation, these expressions of all the zeros to the right-hand side of the decimal point are significant.
For instance, \[6.5 \times {10^3}\] has two significant figures.
\[6.50 \times {10^3}\] has three significant figures.
Lastly, \[6.500 \times {10^3}\] has four significant figures.
So, the no.of significant numbers in \[6.02 \times {10^{23}}\] is 3.
So, option B is correct.

Note: Exact numbers have or demonstrate an infinite number of significant figures. For instance, in 60 pencils or 100 copies, there are unlimited significant figures present as these are exact numbers and can be indicated or represented by documenting an unlimited no.of zeros after positioning a decimal i.e. 50 = 50.000000 or 100 = 100.000000.