Significant Figures | Counting significant figures

What are Significant Figures?

 In the measured value of a physical quantity, the digits about the correctness of which we are sure plus the last digit which is doubtful are called the significant figures.

significant figures

For counting significant figures, we use the following rules:

1.All nonzero digits are significant. For example, x = 1234 has four figures.

2.All zeros occurring in-between the two nonzero digits are significant. For example, x= 20008 has five significant digits.
3.In a number without decimal, zeros on the right of nonzero digit are not significant. (However, when some value is recorded on the basis of actual measurement, the zeros on the right of nonzero digit become significant. For example, m = 100 kg has three significant figures but x = 100 has only one significant digits.)
4.In a number with decimal, zeros on the right of the last nonzero digit are significant. For example, x = 1.58000 has six significant.
5.In a value less than one, zero occurring between the decimal point and nonzero digit on the right are not significant. For example, x = 0.00097, there are two significant. The zero placed (conventionally) to the left of the decimal point is not significant.
6.The change in the units of the measurement of a quantity does not affect the number of significant.

7.When some value is expressed in an exponential form, the exponential term does not affect the number of significant. For example in:
X=23.4=23.4 × 10¹=2.34 × 10²=0.0234 × 10³=0.00234 × 10⁴==234 × 10^-1=2340 × 10^-2=23400 × 10^-3, there are three significant figures only.

Point out the difference between the numbers 4.0 and 4.000 ?

4.0 has only two significant while 4.000 has got four significant figures i.e. measurement 4.0 has been made correct up to first decimal place only, while the measurement 4.000 has been made correct up to fourth decimal place.