01Class 11 Physics

Units and Measurement formulas

The error and dimension formulas you need for Units and Measurement. Small chapter, but its dimensional checks are useful everywhere in Physics.

Free from Anva, anvatechlabs.com

Errors

Absolute error: $\displaystyle \Delta a_i = |a_{\text{mean}} - a_i|$
Relative error: $\displaystyle \delta a = \frac{\Delta a_{\text{mean}}}{a_{\text{mean}}}$
Multiply by 100 for percentage error.
Error in a sum or difference: $\displaystyle \Delta Z = \Delta A + \Delta B$
Absolute errors always add.
Error in a product or quotient: $\displaystyle \frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B}$
Relative errors add.
Error in a power: $\displaystyle Z = \frac{A^p B^q}{C^r} \;\Rightarrow\; \frac{\Delta Z}{Z} = p\frac{\Delta A}{A} + q\frac{\Delta B}{B} + r\frac{\Delta C}{C}$

Subtracting errors when two quantities are subtracted. Errors never cancel, so they always add.
Counting trailing zeros wrongly in significant figures. 0.0230 has three significant figures, and the leading zeros don't count.
Treating a dimensionally correct equation as a proven one. Dimensions can't catch a wrong numerical factor like 1/2.

7 days free when you sign up. No card needed.