Question

A length is quoted as 8.8mm. What is the percentage relative uncertainty implied by this number?

Answer 1

Answer: The percentage relative uncertainty for 8.8mm is 1.1%

Step-by-step explanation: We are given a length which is 8.8mm and we are asked to write the percentage relative uncertainty for this number.

The uncertainty for this number is not specified, then we assume that it is
`\pm {1}` in the final digit of the given number. Hence, the absolute uncertainty associated with the given number will be
`\pm {0.1}mm`

Formula for percentage relative uncertainty is given by:

`\%\text{ relative uncertainty}=\frac{\text{Absolute uncertainty}}{\text{True value}}* 100`

Putting the values, in above equation, we get

`\% \text{ relative uncertainty}=(0.1)/(8.8)* 100`

`\% \text{ relative uncertainty}=1.136\%\approx 1.1\%`