43 Find the absolute and percent relative uncertainly and ex

4-3

Find the absolute and percent relative uncertainly and express each answer with a reasonable amount of significant figures. A. 5.1 (pm0.3) - 3.7 (pm0.2) = B. 8.24 (pm0.04_ times 0.012 (pm0.001) = C. [3.1(pm0.3) - 1.4 (pm0.1)]/8.5(pm0.6) = D. 9.2(pm0.7) times [[5.4(pm0.3) times 10^-3 + [5.6(pm0.1) times 10^-3]] =

Solution

C).

given [3.1 (+/- 0.3) - 1.4(+/-0.1)] / 8.5(+/- 0.6)

Well, if we look at the first one,
3.1 (+/- 0.3 this just means that the value can be anywhere from (3.1 - 0.3 ) to (3.1 + 0.3)
So the range of values is 2.8 to 3.4

now for

1.4(+/-0.1) value will be 1.4 -0.1 to 1.4 +0.1

so the range value is 1.3 to 1.5

and 8.5(+/- 0.6) values will be 8.5 -0.6 to 8,5 to 8.5 + 0.6

so the range values are 7.9 to 9.1

we will just do 3.1 - 1.4 /8.5 = 0.2 this is the expected value

(2.8 - 1.3)/7.9

= 0.19

take max range values (3.4 - 1.5) / 9.1

= 0.208

So the absolute uncertainty is 0.19+/- 0.01 .

To help you remember how to do this kind of thing, just ask yourself what percentage of 10 is 2.
Well, its just

(2 / 10 ) * 100 = 20 %

So what percentage of 0.19 is 0.01?

(0.01 / 0.19) * 100 = 5.26% to three sig figs. giving

0.19 +/- 5.26%

D).

9.2(+/-0.7) x [ 5.4(+/-0.3) x10^-3] + [5.6(+/-0.1)10^-3)]

so 9.2(+/-0.7) the values will be among 9.2 -0.7 to 9.2 +0.7

so the range of values is 8.5 to 9.9

similerly for 5.4(+/-0.3) = 5.4 -0.3 to 5.4 +0.3

range is 5.1 to 5.7

the same for 5.6(+/-0.1) = 5.6 -0.1 to 5.6 +0.1

range is 5.5 to 5.7

now find the normal value= 9.2 x [ 5.4 x 10^-3 + 5.6 x 10^-3 ]

=9.2 x (0.011)

= 0.1012

this is the expected value

now take the minimum range value and find out value

8.5 x [ 5.1 x 10^-3 + 5.5 x 10^-3 ]

8.5 [0.0106]

= 0.901

now take max values of range and do the same procedure

9.9 x [ 5.7 x 10^-3 + 5.7 x10^-3 ]

9.9 [0.0114]

=0.113

So the absolute uncertainty is 0.1012 +/- 0.01

. For the percentage uncertainty, you have to work out what percentage of 0.1012 is 0.01.

To help you remember how to do this kind of thing, just ask yourself what percentage of 10 is 2.
Well, its just

(2 / 10 ) * 100 = 20 %

So what percentage of 0.1012 is 0.01?

(0.01 / 0.1012) * 100 = 9.88% to three sig figs. giving

0.1012 +/- 9.88%