Question with associated uncertainty

[kevinf]

i am having problems with this problem

Time standards are now based on atomic clocks. A promising second standard is based on pulsars, which are rotating neutron stars (highly compact stars consisting only of neutrons). Some rotate at a rate that is highly stable, sending out a radio beacon that sweeps briefly across Earth once with each rotation, like a lighthouse beacon. Suppose a pulsar rotates once every 1.572 806 448 872 75 +/-5 ms, where the trailing +/-5 indicates the uncertainty in the last decimal place (it does not mean +/-5 ms).

(b) How much time does the pulsar take to rotate 1.0 * 10^6 times? (Give your answer to at least 4 decimal places.)

i converted 1.0e6 to ms by multiplying it to the 1.572 806 448 872 75 and then multiplied it to seconds (thats what they want the answer in), but i keep getting the wrong answer. is it because i didn't consider the +/-5. if so how would i do it

 

[mgb_phys]

Because the uncertainty is such a small part of the value you can consider it to just be a multiplicative factor.
Think what percentage of the value the error is, now you answer will have the same error.
eg, if I measure a part to be 1000 +/5 mm and I have a 100 of them the overal length s 100,000 +/- 500mm

 

[kevinf]

but in the question it says it doesn't mean +/- ms though

 

[kevinf]

anyways, any idea on how to do b

 

[mgb_phys]

I was just using whole numbers to simplify the explanation.
If you have a measurement of 1.000 with an uncertainty of 5 in the last place that is just
1.000 +- 0.005 then you have a measurement with an uncertainty of 1 in 1.000/0.005 or 1 in 200 or 0.5%
So if multiply or divide this number to get your final answer that will also have an uncertainty of 0.5%.


The time to rotate 1 million periods is just 1.572 806 448 872 75 * 1million or 1 572 806. 448 872 75 but since they ask for 4 decimal places 1 572 806. 448 9 , you can ignore the uncertainty because it is much less than the number of decimal places you have given.

I know this seems a bit silly and pointless but knowing about what accuracy you should quote and how errors propagate is the most important thing in any experimental science.
It really is vital to get a good understanding of it.

 

[kevinf]

yeah that's the answer that i got before too but it wasn't right

 

[kevinf]

nvm i forgot to convert to sec which i forgot to post in my original question

 

[kevinf]

so the associated uncertainty would be 1.572 806 448 872 75 / .00000000000005 seconds?