# Lab report problem ?

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.

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.

Homework Helper
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" [Broken]

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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.