Difference between Significant figure and Order of magnitude
Significant figure
- Significant figure explains us accuracy of measurement of a physical quantity.
- The number of digits in a measurement about which we are certain which is added with one additional digit about which we are not certain is known as significant figures or significant digits.
Eg. If any calculation has readings as 45.5, 45.5 and 45.6 then the mean of this will be 45.33. In this calculation digits 4 ,5 are certain but we are not sure about accuracy of last two digits i.e. 3 , 3. So in this calculation number of significant digits is 4.
- More the significant figures obtained in a measurement, more is the accuracy in measurement.
- All non zero digits in measurement are taken as significant figures.
Eg. If the cross-section area of wire is measured as 23.653 cm2, then the number of significant figures is 5.
- Zeros which comes between two non-zero digits are taken as significant figures.
Eg. The number of significant digits in calculation 150.03 is 5.
Significant figure
- To avoid the difficulties found in representation of large number of significant digits in calculation, the calculations are used in certain scientific notation.
- Representation of calculation in measurement in closest power of 10 is known as order of magnitude.
Eg. Mass of electron is 0.000000000000000000000000000000931 kg, which is inappropriate and time consuming; hence the same value can be written as,
9.31×10-31 kg.
- When the first digit in the measurement is less than five then the decimal point should be shifted after that digit and then should be represented in the closest power of 10.
Eg. The following measurements can be written in terms of order of magnitude as,
- 23564 m = 2.3564×104 m, hence order of magnitude is 104 m
- 00035 g= 3.5×10-4 g, hence order of magnitude is 10-4 m
- When the first digit in the measurement is greater than five then the decimal point should be shifted before that digit and then should be represented in the closest power of 10.
Eg. The following measurements can be written in terms of order of magnitude as,
- 640000 m = 0.64×106 m, hence order of magnitude is 106 m
- 00865 g= 0.865×10-2 g, hence order of magnitude is 10-2 g