Calculating Percentage Uncertainty for Measured Lengths

[calculator20]

Two lengths, a and b, are measured to be 51+/-1cm and 49+/-1cm respectively. In which of the following is the percentage uncertainty the largest?

A a+b
B a-b
C a x b
D a/b

The answer should be b but I can't figure out why. I know that for / and x you add the percentage errors so if the error is approx 2% then each of C and D have errors of 4% of their answers ie

C 51 x 49 = 2499 and 4% is ~100
D 51/49 = 1 and 4 % is 0.04

I think that for + and - you add absolute uncertainties ie 0,02 + 0.02 = 0.04 ie

A 51 + 49 = 100 and 100 x 0.04 = 4
B 51 - 49 = 2 and 2 x 0.04 = 0.08

But that makes C the largest error.

What am I missing here? It's supposed to be multiple choice, non calculator so I'm probably overthinking it?

 

[BvU]

Don't see how absolute uncertainties of 1 each can add up to 0.04 ...

 

[haruspex]

C 51 x 49 = 2499 and 4% is ~100

100 is the absolute error. You are only interested in percentage errors, so stop the calculation at 4%.

Don't see how absolute uncertainties of 1 each can add up to 0.04 ...

I'm guessing calculator20 is considering +/-1 as a range of 2.

 

[BvU]

I think that for + and - you add absolute uncertainties ie 0,02 + 0.02 = 0.04

@calc: 0.02 is the relative error! You want the absolute error here !

for error read uncertainty - saves confusion

 

[HallsofIvy]

Two lengths, a and b, are measured to be 51+/-1cm and 49+/-1cm respectively. In which of the following is the percentage uncertainty the largest?

A a+b

Then a+ b= 100 +/- 2 cm (NOT 4) so the percentage error is 2/100= 2%

B a-b

a- b= 2+/- 2 cm so the percentage error is 2/2= 100%

C a x b

D a/b

The percentage errors for a and b separately are 1/51= 0.0196 or about 2% and 1/49= 0.02041 or about 2% so the percentage errors of a x b and a/b are 2+ 2= 4%

The answer should be b but I can't figure out why. I know that for / and x you add the percentage errors so if the error is approx 2% then each of C and D have errors of 4% of their answers ie

C 51 x 49 = 2499 and 4% is ~100
D 51/49 = 1 and 4 % is 0.04

I think that for + and - you add absolute uncertainties ie 0,02 + 0.02 = 0.04 ie

A 51 + 49 = 100 and 100 x 0.04 = 4
B 51 - 49 = 2 and 2 x 0.04 = 0.08

But that makes C the largest error.

What am I missing here? It's supposed to be multiple choice, non calculator so I'm probably overthinking it?

 

[BvU]

@Ivy: I thought we wanted calc to learn something, not have the answers dumped in his lap !

 

[BvU]

All in good spirit, of course...

 

[calculator20]

Thank you everyone. I'd gone with fractions rather than whole values. I can see where things went wrong now. Many thanks!