evaporade's demonstration of applicability of sig figs

[evaporade]

How many significant figures in each of the natural numbers 17 and 117 ?

[monokekie]

17===> 2 sig fig
117====> 3 sig fig

 

[evaporade]

Now find 17 X 117, to the correct number of significant figures.

[shinny]

[monokekie]

ohh btw, dodgy txt books can be ambiguous sometimes, so don't worry too much, follow the rules would do. =]

[evaporade]

there are 17 rows and each row has 117 poles. How many poles are there?

[shinny]

Keep in mind that most textbooks and past exam papers don't consider sig figs, but you need to.

there are 17 rows and each row has 117 poles. How many poles are there?

I think you're getting confused with the application of sig figs. You don't need to consider them here.

[evaporade]

You always do when working with measured quantities. So when do you think you need to consider significant figures?

[evaporade]

I think the last question is too difficult. Try this one: What is the total length of exactly 17 poles each measured 1.170 m, to the correct number of significant figures?

[shinny]

So when do you think you need to consider significant figures?

When you're working with non-discrete values I assume. A quick googling seems to prove this. So unless you start to consider the possibility of having half a pole or something, I wouldn't really consider any need for sig figs for a calculation like that.

[evaporade]

Once again you always do when working with measured quantities. To know why, you need to understand the meaning and use of significant figures. By the way,
17 X 1.170 = 2.0 X 10 metres is wrong.

[shinny]

Once again you always do when working with measured quantities. To know why, you need to understand the meaning and use of significant figures. By the way,
17 X 1.170 = 2.0 X 10 metres is wrong.

Oh whoops, contradicted myself by counting the sig figs in 17 (which you stated was exactly anyhow). 19.89 metres then. However, for discrete objects, my assumption is that there's no margin of error (unless the person counting can't count) and you don't consider sig figs. A few other sources which agree are;

Note that exact numbers obtained by counting discrete objects are not subject to the rules of significant figures and should be expressed as exact integers.

And from Victorian Science themselves;

Unless we are counting discrete, known quantities such as the number of students enrolled at the school, when we measure quantities on instruments, the last figure in the measurement is usually uncertain.

[evaporade]

Once again you always do when working with measured quantities.

Quote from: http://www.statemaster.com/encyclopedia/Significant-digits
Note that exact numbers obtained by counting discrete objects are not subject to the rules of significant figures and should be expressed as exact integers.

This is just a lazy way to deal with significant figures.

A natural number has infinite number of significant figures.
For example 17 = 16.99999999999999......................

Back to the original question.
17 has infinite number of s.f.
117 has infinite number of s.f.
Hence 17 x 117 = 1989 has infinite number of s.f.

So there is no need to make any exceptions. You always do when working with measured quantities.

[shinny]

Once again you always do when working with measured quantities.

Quote from: http://www.statemaster.com/encyclopedia/Significant-digits
Note that exact numbers obtained by counting discrete objects are not subject to the rules of significant figures and should be expressed as exact integers.

This is just a lazy way to deal with significant figures.

A natural number has infinite number of significant figures.
For example 17 = 16.99999999999999......................

Back to the original question.
17 has infinite number of s.f.
117 has infinite number of s.f.
Hence 17 x 117 = 1989 has infinite number of s.f.

So there is no need to make any exceptions. You always do when working with measured quantities.

So you asked these questions just to play people around on technicalities (of which I'm not sure I agree with anyway)? I thought you were actually looking for the answers yourselves. As for the original question, of course it depends WHERE you got these numbers from. The two clearly aren't considered to have an infinite number of sig figs if they were obtained say, from a scale which only gets accuracy to each single gram, so anything between approximately 16.5 to 17.5 would round to 17. If these numbers were obtained from this scale, clearly they don't represent something with an infinite number of sig figs. And really, if you're going to so vehemently disprove what I've said, can you give some evidence? I wouldn't mind learning something new myself, but I'm not going to change my position just because you're basically saying "that's how it is".

[evaporade]

This forum is not only about getting help for some questions. One can express ideas through questions.

'Note that exact numbers obtained by counting discrete objects are not subject to the rules of significant figures and should be expressed as exact integers.' This is a bit like "just do it, you'll get the right answer'.

'The two clearly aren't considered to have an infinite number of sig figs if they were obta...' I don't think you read the original question carefully enough.

By saying this 'so anything between approximately 16.5 to 17.5 would round to 17', I don't think you know how to work with sig. fig. Correctly, 17.0 .