Physics Class 11 Chapter 2. Units and Measurements | Page 14

Criteria
Sum or Difference
Product
Raised to Power
Resultant value
Z
Z = A ± B
Z = AB
Z = A k
Result with error
Z ± ΔZ =( A ± ΔA) +( B ± ΔB)
Z ± ΔZ =( A ± ΔA)( B ± ΔB)
Z ± ΔZ =( A ± ΔA) k
Resultant error range
± ΔZ = ± ΔA ± ΔB
ΔZ / Z = ΔA / A ± ΔB / B
Maximum error ΔZ = ΔA + ΔB
ΔZ / Z = ΔA / A + ΔB / B ΔZ / Z = k( ΔA / A)
Error
Sum of absolute errors
Sum of relative errors
k times relative error
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 o All non-zero digits are significant.