Every measurement results in a number that includes reliable digits and uncertain digits. Reliable digits plus the first uncertain digit are called significant digits or significant figures.These indicate the precision of measurement which depends on least count of measuring instrument.
Example, period of oscillation of a pendulum is 1.62 s. Here 1 and 6 are reliable and 2 is uncertain. Thus, the measured value has three significant figures.
Rules for determining number of significant figures
- All non-zero digits are significant.
- All zeros between two non-zero digits are significant irrespective of decimal place.
- For a value less than 1, zeroes after decimal and before non-zero digits are not significant. Zero before decimal place in such a number is always insignificant.
- Trailing zeroes in a number without decimal place are insignificant.
- Trailing zeroes in a number with decimal place are significant.
Cautions to remove ambiguities in determining number of significant figures
- Change of units should not change number of significant digits. Example, 4.700m = 470.0 cm = 4700 mm. In this, first two quantities have 4 but third quantity has 2 significant figures.
- Use scientific notation to report measurements. Numbers should be expressed in powers of 10 like a x 10b where b is called order of magnitude. Example, 4.700 m = 4.700 x 102 cm = 4.700 x 103 mm = 4.700 x 10-3 In all the above, since power of 10 are irrelevant, number of significant figures are 4.
- Multiplying or dividing exact numbers can have infinite number of significant digits. Example, radius = diameter / 2. Here 2 can be written as 2, 2.0, 2.00, 2.000 and so on.