# Unit, Dimension & Error

#### Fractional and Percentage Errors

5.1 If Δx is the error in measurement x, then
Fractional error =
Percentage error = × 100
Percentage error in experimental measurement
=
5.2 PROPAGATION OF ERROR (ADDITION AND SUBTRACTION) :
Let error in x is ± Δ x, and error in y is ± Δy, then the error in x + y or x  y is ± (Δx + Δy). The errors add.
5.3 MULTIPLICATION AND DIVISION :
Let errors in x, y, z are respectively ± Δx, ± Δy and ± Δz. Then error in a quantity f (defined as)
f = is obtained from the relation

The fraction errors (with proper multiples of exponents) add. The error in f is ± Δf.

Important Points :
(a) When two quantities are added or subtracted the absolute error in the find is the sum of the absolute error in the quantities.
(b) When two quantities any multiplied or divided, the fractional error in the result is the sum of the fractional error in the quantities to be multiplied or to be divided.
(c) If the same quantity x is multiplied together n times (i.e. xn), then the fractional error in xn is n times the fractional error in x,
i.e. ± n

#### IIT (Class X)

• Unit, Dimension & Error
• Vectors
• Motion in One Dimension
• PROJECTILE MOTION
• NEWTON'S LAWS OF MOTION & FRICTION
• WORK, POWER, ENERGY & CONSERVATION LAWS
• CIRCULAR MOTION & ROTATIONAL DYNAMICS
• GRAVITATION