How do you work out percentage errors???

I doing some AS coursework at the moment - measuring the young modulus of a rubber band. I'm really confused because I not sure on how to work out the percentage error of the metre ruler I used. I took two readings from the metre ruler (top and bottom of rubber band) and the extension was calculated. Which figures do I use? Help!

Reply 1

Morbo

Estimating errors is quite subjective at A-level and even in 1st year undergrad. For a metre rule, it's generally accepted that you can "read" to the nearest two millimetres if the smallest graduations are centimetres, and you can read to the nearest 0.5mm if the smallest graduations are millimetres.

Your "percentage error" is the fraction that the estimated error makes up of your reading.

So let's go with the example of being able to read to the nearest 2mm. If I measure the length of my band to be 420.0mm, then the reading could actually be anywhere between 419mm and 421mm. So we say the reading is 42mm +/- 1mm.

As a percentage error, this is +/- (1mm/420mm) * 100 = +/- 0.2%

Reply 2

strawberry

percentage error is how off you are over accepted value multiplied by 100. ain't it? :P or are you talking about percentage error in readings?

Reply 3

Morbo

strawberry

percentage error is how off you are over accepted value multiplied by 100. ain't it? :P or are you talking about percentage error in readings?

no, i don't believe that is the definition. the idea is that you're a scientist and you are MEASURING this value - it doesn't matter what the accepted value is. if you can show that your experiment has a suitably small error, then your value might even become the accepted value!

another point i forgot to mention is that when you have a nominal error such as +/- 1mm in your readings, obviously it makes sense to try and get as large a value as possible so that this error becomes small as a percentage of your reading. if you used your metre rule to measure something 5mm long with error +/- 1mm, you'd have percentage error of 20%, which is rubbish. if you can measure to +/- 1mm and you're measuring the distance from the Earth to the Moon, then your percentage error is very small indeed.

okay

thanks for your help. I 've worked out my percentage errors for the metre ruler - now I have to work them out for the actual readings so I think it is alright to get high percentage errors like 20% or more. When measuring the young modulus using a rubber band, how would you minimise errors? All I could think of was to use a vernier scale instead of a metre ruler. Is there anything else???

thanks :smile:

Reply 6

Morbo

it'd help if you show us your working. you shouldn't really be getting 20% errors!