# Measurements and significant figures

Pho Tek
Ranch Hand
Posts: 782
I just read Markcc's blogpost on significant figures.

I have a question that I hope javaranchers can help me out.

if you've got a measured value of 2.42532, with six significant figures, and you need to round it to 3 significant figures ...

In scientific experiments, how do you actually perform a measurement to a specific precision (in the case above, 6 sigfigs) ?
Is this possible only scientific equipment ? e.g. If I buy a simple plastic ruler from a book store, how do I know what precision I have at my disposal ?

Regards,

Pho

David O'Meara
Rancher
Posts: 13459
If you have one mark every 30cm, you can measure the numbers 0 to 30 (1 to 2 sigfigs)
If you have millimeters, you can measure 301 values from 0.0 to 30.0 (2 to 3 sig figs)
The better the graduation on the rule and your ability to read those values, the more significant your measurements will be.

Pat Farrell
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Pho Tek wrote: If I buy a simple plastic ruler from a book store, how do I know what precision I have at my disposal ?

The number of digits is controlled by two things: the tool used to measure, and the skill of the person making the measurement.

If the ruler has markings for each millimeter, then the finest measurement will be in millimeters. If you are measuring a distance of 1.234 meters, you have three significant digits. (it had better be a long ruler).

Its more complicated, as a really cheap ruler may not actually measure in meters/millimeters, but some error number (assume it is 50% off) then you will write done a lot of significant digits from your measurement, but few (none?) are accurate.

Someone with a good rule, good eyes, and skill may be able to see that rather than being about ten millimeters long, its really a bit longer, and so they can write down 10.2 milimeters. This means that there are two significant digits. The "2" may be wrong, but its much more likely to be 1 or 3, and its unlikely to be 10.7

Pho Tek
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Posts: 782
Thanks @David @Pat.

How do you learn such things ?

Pat Farrell
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I was taught most of this in freshman Engineering. Nearly four decades ago. This was back when engineers used slide rules, and you had to understand significant digits. If you were good, you could get as much as three and a half digits out of a good slide rule.

Later, when I was interning at an Engineering firm, the basic four function calculators came out. I forget how expensive they were, but they were so expensive that in a department with 15 engineers and maybe 20 draftsmen, we had two.

We also had a Korean Engineer who used an abacus. So naturally, we had a race. Calculator vs abacus.

The guy with the abacus won.

Henry Wong
author
Marshal
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Is this possible only scientific equipment ? e.g. If I buy a simple plastic ruler from a book store, how do I know what precision I have at my disposal ?

I had to do something similar back in college. For a chemistry lab, we have to report the precision of all measurements. But many of the measurements were just temperatures -- how do you report the precision of a thermometer?

In the end, I just got all the lab partners to report the temperature as best as he/she could. The official recorded temperature was the mean (along with the standard deviation) of all the sampled readings.

Henry

Bert Bates
author
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Once you've figured this out, you can determine how long the coast of England is...

Pat Farrell
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Aren't all coastlines fractal?

fred rosenberger
lowercase baba
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Wikipedia has a decent article on sig figs.