Class 11 Physics Units and Measurements | Significant Figures |

__Significant Figures__

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 10**where b is called^{b}**order of magnitude**. Example, 4.700 m = 4.700 x 10^{2}cm = 4.700 x 10^{3}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.

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