**Combination of Errors**

(i) **Error in Addition or Subtraction** :

Let x = a + b or x = a- b

If the measured values of two quantities a and b are (a ± Δa) and (b ± Δb), then maximum absolute error in their addition or subtraction is

Δx = ± (Δa + Δb)

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

## Combination of Error Formula, Definition, Rules

(ii) **Combination of Errors ****in Multiplication or Combination of Errors in Division:
**Let x = a x b or x = \(\frac{a}{b}\)

If the measured values of a and b are (a ± Δa) and (b ± Δb), then maximum relative error

\(\left(\frac{\Delta a}{a}+\frac{\Delta b}{b}\right)\)

(iii) **Error in case of a measured quantity raised to a Power:
**Let z = a

^{p}b

^{q}/ c

^{r}

If the measured values of a, b and c are (a ± Δa), (b ± Δb) and (c ± Δc), then maximum error

\(\frac{\Delta z}{z}=p\left(\frac{\Delta a}{a}\right)+q\left(\frac{\Delta b}{b}\right)+r\left(\frac{\Delta c}{c}\right)\)

**Note:** The smallest value that can be measured by a measuring instrument is called least count of that instrument, eg. A metre scale having graduation at 1 mm division scale spacing, has a least count of 1 mm or 0.1 cm.

**Units and Measurement Topics:
**Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units | Systems of Units |

Dimensions | Significant Figures |

Rounding off | Error |

Combinations of Errors |