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# Given the numbers: 161, 0.161 and 0.0161. The number of significant figures for the three numbers is:A. 3,4 and 5 respectivelyB. 3,3 and 3 respectivelyC. 3,3 and 4 respectivelyD. 3,4 and 4 respectively

Last updated date: 21st Jun 2024
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Hint: Significant figures is defined as the total number of certain digits plus one doubtful digit (in a number used to express a measurement).
The following rules should be observed for reporting the number of significant figures while expressing the result of a measured quantity.
Non- zero integers: - All non-zero digits are significant. For example, 552 has three significant figures.
Zeros: - There are three types of zeros:
Leading zeros: - These are the zeros that precede all the non-zero digits and these do not count as significant figures. For example, 0.05 has one significant figure.
Captive zeros: - These are the zeros that can be found between non- digits and they always count as significant figures. For example, 2007 has four significant figures.
Trailing zeros: - These are the zeros that can be found at the right end of the number and they are significant if the number contains a decimal point. For example, 0.1000 has three significant figures.
The greater number of zeros to the right of the decimal point indicates greater measurement accuracy.
Exact numbers: - Many times calculations involve numbers that were not obtained using measuring devices but were determined by counting: 10 oranges, 12 eggs, 3 apples, etc. Such types of numbers are called exact numbers. Other examples of exact numbers are 2 in $2\pi r$ (the circumference of a circle).
Exponential notation: - In the exponential notation, the numerical portion represents the number of significant figures. Therefore, only those zeros are included in the numerical portion which is significant. Thus, if the value of 5000 has indeed been determined to four significant figures, it is indicated as $5.000 \times {10^3}$. If it is determined to three significant figures, it is indicated as $5.00 \times {10^3}$ and so on.

Complete step by step answer:
In 161 it contained three non-zero digits and as we know all non-zero digits are significant. So, 161 has 3 significant figures.
In 0.161 it contains one zero before the decimal point and three non-zero digits. As we know zero before the decimal point is insignificant but the non-zero digits after the decimal point are significant. So, 0.161 has three significant figures.
In 0.0161 it contains two zeros in which one is before and the other one is after the decimal point with three non-zero digits after the decimal points. As we know zero before and after the decimal point is insignificant but the non-zero digits after the decimal point are significant. So, 0.0161 has three significant figures
Therefore the significant figures of 161, 0.161, and 0.0161 have 3, 3, and 3 significant figures respectively.

Thus, the correct option for this question is B.

Note: A calculation involving significant figures are guided by the following rules:
Rule 1: The result must be reported to the same number of decimal places as that of the term with the least number of decimal places while carrying addition or subtraction of several terms.
Rule 2: The number of significant figures in the final answer should not be greater than the number of significant figures in the least precise factor in case of the calculations involving multiplication or division.