SIGNIFICANT FIGURES : Definition and Rules for counting significant figures

SIGNIFICANT FIGURES

Definition and Rules of Significant Figures

Suppose we ask three students to measure the length of a stick using metre scale (the least count for metre scale is 1 mm or 0.1 cm). So, the result of the measurement (length of stick) can be any of the following, 7.20 cm or 7.22 cm or 7.23 cm. Note that all the three students measured first two digits correctly (with confidence) but last digit varies from person to person. So, the number of meaningful digits is 3 which communicate both measurement (quantitative) and also the precision of the instrument used. Therefore, significant number or significant digit is 3.

It is defined as the number of meaningful digits which contain numbers that are known reliably and first uncertain number.

Examples: The significant figure for the digit 121.23 is 5, significant figure for the digit 1.2 is 2, significant figure for the digit 0.123 is 3, significant digit for 0.1230 is 4, significant digit for 0.0123 is 3, significant digit for 1230 is 3, significant digit for 1230 (with decimal) is 4 and significant digit for 20000000 is 1 (because 20000000 = 2 × 10⁷ has only one significant digit, that is, 2).

In physical measurement, if the length of an object is l = 1230 m, then significant digit for l is 4.

Rules for counting significant figures:

i) All non-zero digits are significant.

Example: 1342 has four significant figures.

ii) All zeros between two non-zero digits are significant.

                Example: 2008 has four significant figures.

iii) All zeros to the right of a non-zero digit but to the left of a decimal point are significant.

Example: 30700. has five significant figures

iv) For the number without a decimal point, the terminal or trailing zero(s) are not significant.

Example: 30700 has three significant figures

v) If the number is less than 1, the zero (s) on the right of the decimal point but to left of the first

non zero digit are not significant.

Example: 0.00345 has three significant figures

vi) All zeros to the right of a decimal point and to the right of non-zero digit are significant.

Example: 40.00 has four significant figures and 0.030400 has five significant figures

vii) The number of significant figures does not depend on the system of units used

Example: 1.53 cm, 0.0153 m, 0.0000153 km, all have three significant figures

 

Note 1: Multiplying or dividing factors, which are neither rounded numbers nor numbers representing

measured values, are exact and they have infinite numbers of significant figures as per the situation.

For example, circumference of circle S = 2πr, Here the factor 2 is exact number. It can be written as 2.0, 2.00 or 2.000 as required.

Note 2: The power of 10 is irrelevant to the determination of significant figures.

For example, x = 5.70 m = 5.70 × 10² cm = 5.70 × 10³ mm = 5.70 × 10⁻³ km. In each case the number of significant figures is three.

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