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 .