Question

Convert the following to relative uncertainties
a) 2.70 ± 0.05cm
b) 12.02 ± 0.08cm

Answer 1

data which is expressed in form of following way

`a = a_o + \Delta a`

here in above expression

`a_o` = true value

`\Delta a` = uncertainty in the value

now the relative uncertainty is given as

`(\Delta a)/(a_o)`

now by above formula we can say

a) 2.70 ± 0.05cm

here

True value = 2.70

uncertainty = 0.05

Relative uncertainty =
`(0.05)/(2.70)` = 0.0185

b) 12.02 ± 0.08cm

here

True value = 12.02

uncertainty = 0.08

Relative uncertainty =
`(0.08)/(12.02)` = 0.00665