Question

Describe what is meant by significant figures and order of magnitude.

Answer 1

Significant figures:

1. Significant figures in the measured value of a physical quantity is the sum of reliable digits and the first uncertain digit.
   OR
   The number of digits in a measurement about which we are certain, plus one additional digit, the first one about which we are not certain is known as significant figures or significant digits.
2. Larger the number of significant figures obtained in a measurement, greater is the accuracy of the measurement. The reverse is also true.
3. If one uses the instrument of smaller least count, the number of significant digits increases.

Rules for determining significant figures:

1. All the non-zero digits are significant, for example if the volume of an object is 178.43 cm3, there are five significant digits which are 1,7,8,4 and 3.
2. All the zeros between two nonzero digits are significant, eg., m = 165.02 g has 5 significant digits.
3. If the number is less than 1, the zero/zeroes on the right of the decimal point and to the left of the first nonzero digit are not significant e.g. in 0.001405, significant. Thus the above number has four significant digits.
4. The zeroes on the right hand side of the last nonzero number are significant (but for this, the number must be written with a decimal point), e.g. 1.500 or 0.01500 both have 4 significant figures each.
   On the contrary, if a measurement yields length L given as L = 125 m = 12500 cm = 125000 mm, it has only three significant digits.

Order of magnitude:
The magnitude of any physical quantity can be expressed as A × 10n where ‘A’ is a number such that 0.5 ≤ A < 5 then, ‘n’ is an integer called the order of magnitude.
Examples:

1. Speed of light in air = 3 × 108 m/s
   ∴ order of magnitude = 8
2. Mass of an electron = 9.1 × 10-31 kg
   = 0.91 × 1030 kg
   ∴ order of magnitude = -30