Error Analysis: Lab Report Decimal Places

[ngkamsengpeter]

Hello , i just doing a experiment on error analysis and i am using meter rule .
The problem i am facing is , since i use meter rule to measure length and for example i get a result of 115.65cm . After that , i want to convert it to meter , actually how many decimal places should i put in my laboratory report ? Someone tell me that i should put 3 or less decimal place but i think we can measure up to 0.0005m using a meter rule , so we should put 4 decimal places . Am i right ?

Besides , the result i need to use to calculate the average length . Then is it the average length is also use 4 decimal places ?

After that , we need to calculate the variance . How many decimal places should i put in the variace ?

After that , we square root the variance to get the standard deviation .Again how many decimal place should i put for the answer of standard deviation ?

Finally , we will calculate the standard error , What is the decimal places should i put for the standard error ?

And for the final answer , should i put (1.1565 +- standard error) m or otherwise ?

I know this is a simple question for physics but i still don't know even i am a undergraduate student now because for the secondary school , our education system don't enforce this rule , so no one use it.

So, somebody please answer my questions .Please.

 

[Sojourner01]

The nearest graduation on a metre rule is the millimetre, so yes you're right, your maximum graduation error is +- 0.5mm. Since this means you're measuring whole numbers of millimetres, you're using 3 decimal places i.e. the closest you can come is (say) 509mm = 0.509m. That's 3 decimal places.

 

[ngkamsengpeter]

The nearest graduation on a metre rule is the millimetre, so yes you're right, your maximum graduation error is +- 0.5mm. Since this means you're measuring whole numbers of millimetres, you're using 3 decimal places i.e. the closest you can come is (say) 509mm = 0.509m. That's 3 decimal places.

Why don't we use 4 decimal places since if i convert 116.25cm to meter is 1.1625 meter ?Do you mean i should round up to 1.163 meter ?

 

[Sojourner01]

Because you're not measuring 116.25cm. You're measuring 116.3cm because your metre rule is accurate to the nearest milllimetre. So yes; you're rounding up. I'd be interested to know what the logic is in making measurements to the nearest 0.5mm.

 

[ngkamsengpeter]

Because you're not measuring 116.25cm. You're measuring 116.3cm because your metre rule is accurate to the nearest milllimetre. So yes; you're rounding up. I'd be interested to know what the logic is in making measurements to the nearest 0.5mm.

Because i see a book say that we use the uncertainty as the half the smaller scale in meter rule.

 

[andrevdh]

A measurement should be given in the format:

measurement +/- uncertainty in the measurement

for example

123.4 +/- 0.2 mm

in such a case there is clearly a measure of uncertainty in the final digit (4) of the measurment. That is why it is sensible to estimate the final digit (fractional part of a millimeter) when measuring with a ruler.

Have a look at this award winning site

http://antoine.frostburg.edu/chem/senese/101/measurement/index.shtml"

 

[Sojourner01]

Because i see a book say that we use the uncertainty as the half the smaller scale in meter rule.

Indeed. That's exactly what you're doing. This is because the greatest distance a measurement can possibly be from one of the small graduations is 0.5mm. A measurement rounded to the nearest millimetre could be a minimum of 0.5mm less than that number, or a maximum of 0.5mm greater.