Question

How many significant figures are there in the measurement 0.020 km?

Answer 1

Hint: Significant figures are meaningful digits which are known with certainty. The number of significant figures in measurement is the number of figures that are known with certainty plus one that is uncertain, beginning with the first non-zero digit. e.g., 8.00 has three significant figures.

Complete step by step answer:
To determine the significant figures in a suitable quantity, following rules are to be applied:
(1) All non-zero digits are significant. For example, 175 cm, 0.175 cm and 1.75 cm all have three significant figures.
(2) Zeros to the left of the first non-zero digit in the number are not considered as significant. Such zero indicates the position of the decimal point.
For example, 0.0165 cm has three significant figures and 0.0027 cm has two significant figures.
(3) Zeros between two non-zero digits are significant.
For example, 1.007 cm has four significant figures. 1.07 cm has three significant figures.
(4) Zeros at the right or end of a number are considered to be significant based on the condition that they belong to the right side of the decimal point. For example, 7.00 cm has three significant figures and 0.080 cm has two significant figures.
But if the terminal zeros are not significant if there is no decimal point e.g., 100 has only one significant figure.
(5) Exact numbers posess or show an infinite number of significant figures.
For example, in 5 pens or 50 copies, there are infinite significant figures present because these are exact numbers and can be shown or represented by writing infinite number of zeros after placing a decimal i.e. 5 = 5.0000 or 60 = 60.00000
The ambiguity in the last point can be removed by expressing the number in scientific notation.
For example, we can express 4500 m in scientific notation in the following forms depending upon whether it has two, three or four significant figures.
$4.5\times {{10}^{3}} m$(Two significant figures)
$4.50\times {{10}^{3}} m$4.50 x 103 m (Three significant figures)
$4.500\times {{10}^{3}} m$ (Four significant figures).
In these expressions all the zeros to the right of the decimal point are significant.
So from these rules we can conclude that there are 2 significant figures in 0.020 km, which is our required answer.

Note: When operators like addition, subtraction, multiplication or division is performed, you need to make sure that the significant figures are rounded off to the nearest and smallest decimal units, for the ease of calculation.