(a) Unit: An arbitrarily chosen standard of measurement of a quantity, which is accepted internationally is called unit of the quantity. The units in which the fundamental quantities are measured are called fundamental or base units and the units of measurement of all other physical quantities, which can be obtained by a suitable multiplication or division of powers of fundamental units, are called derived units.
(b) Rounding – off: In no case should the result have more significant figures than die figures involved in the data used for calculation. The result of calculation with numbers containing more than one uncertain digit should be rounded off. The rules for rounding off are given below.
|
Rule |
Example |
| (i) |
If the digit to be dropped is smaller than 5, then the preceding digit should be left unchanged. |
(i) 7.32 is rounded off to 7.3
(ii) 8.94 is rounded off to 8.9 |
| (ii) |
If the digit to be dropped is greater than 5, then the preceding digit should be increased by 1 |
(i) 17.26 is rounded off to 17.3
(ii) 11.89 is rounded off to 11.9 |
| (iii) |
If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit should be raised by 1 |
(i) 7.352, on being rounded off to first decimal becomes 7.4
(ii) 18.159 on being rounded off to first decimal, become 18.2 |
| (iv) |
If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is not changed if it is even |
(i) 3.45 is rounded off to 3.4
(ii) 8.250 is rounded off to 8.2 |
| (v) |
If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is raised by 1 if it is odd |
(i) 3.35 is rounded off to 3.4
(ii) 8.350 is rounded off to 8.4 |
(c) Dimensionless quantities: On the basis of dimension, dimensionless quantities are classified into two categories.
(i) Dimensionless variables:
Physical quantities which have no dimensions, but have variable values are called dimensionless variables. Examples are specific gravity, strain, refractive index etc.
(ii) Dimensionless Constant:
Quantities which have constant values and also have no dimensions are called dimensionless constants. Examples are π, e, numbers etc.
