Question

What are the rules to determine the significant figures? Explain each rule by giving examples.

Answer 1

Significant figures are defined as the total number of digits in a particular number (generally, this number is a value of measurement ) that contributes to the degree of accuracy of that particular value. There are certain rules that govern the counting of significant numbers in a value but the most important of them is, “we always start counting at the first non-zero number”.

Complete step-by-step solution:
The counting of significant figures in a number is governed by certain rules which impose certain conditions. Let us understand these one by one with the help of some examples. This is done as follows:
(1) Non-zero numbers are always significant in any case. For example: 342.87 has five significant numbers.
(2) Zeroes placed between two significant numbers are significant. For example: 34.02 has four significant numbers. Another example could be: 500.004 has six significant figures.
(3) Zeroes whose leads are not any significant numbers are insignificant. For example: 0.00009 has only one significant number.
(4) Zeroes to the right of any non-zero number after the decimal point are considered as significant but zeroes at the end of whole numbers are considered insignificant. For example: 0.0560 has three significant numbers whereas 300 has only one significant number.
(5) The number of significant numbers remains even after change of units. For example: 1cm is equal to 0.01m . In both the measurement values, the number of significant numbers is the same, that is, equal to one.
Hence, we have seen all the rules are necessary for determining the number of significant numbers with the help of some examples.

Note: The concept of counting significant numbers is very important in the field of measurement and statistical data analysis. One last example to understand our concept would be of: 0.000 . This number contains zeros after decimal to the end, so it is a controversy between point number (3) and (4). Here, the number of significant figures is zero because there is no non-zero number which can be termed significant.