I had a follow up post to last nights Sign. Dig. post, that I seem to have deleted. First I wanted to get everyone on the same page about sign. dig.s which we seem to be. Now to the real question:
547.34' * 1.9' = ?
Your responses please.
Stephen
> I had a follow up post to last nights Sign. Dig. post, that I seem to have deleted. First I wanted to get everyone on the same page about sign. dig.s which we seem to be. Now to the real question:
>
> 547.34' * 1.9' = ?
Stephen, your post is still there. My answer remains the same to the product of 547.34 ft. and 1.9 ft., too.
1040 s.f +/- 30 s.f.
or
0.024 ac.
My Question For Stephen Is ?
If you can measure the 547.34' to 2 decimals, why can't you measure 1.9' to the same 2 decimals?
You have one number with a precision of 1:5000 and a second with a precision of 1:20. Would you not expect a lot of slop in any combination of mathematical manipulations with those values?
You keep asking this question so it may be obvious to some that you want a different answer. We will oblige you, "OK Stephen, what answer do you want?"
Paul in PA
Applying the rule of sig figs to survey computations doesn't always provide meaningful data. If both numbers are measured quantities, then some expression of uncertainty should be expressed to be able to display numbers of greater digits than sig figs rule would allow. Assuming the more precise measure has a +- deviation of 0.005', and the other is around +- 0.05', your uncertainty in s.f. would be 27 conservatively. If the lesser measure could have been stated to the hundreth, the uncertainty changes by an order of magnitude, making it (uncertainty) much less consequential. Were it me, I would state the area as being 1040 sf, +- 27 s.f. Elsewise, I'd get a more precise measure than 1.9'
If you can't measure under 2 foot to a hundredth, you shouldn't be surveying!
😉
I didn't see the first post, so I don't understand the smartass replies...
The answer is 1039.9. The answer can only be expressed to the same accuracy as the least accurate number involved.
Jim
^ you might wanna review the rules of significant figures
Jim ?
If this were a simple math problem
547.34 * 1.9 = 1039.946
Rounding to 1039.9 is too generous for the information given, i.e. 1.9 is only 1:20 precision.
Kent is being generous in stating the answer is 1040 but it makes more sense to use that value than the 1000 that the input requires.
In surveying we should be able to make all measurements to within 0.01, carry 0.0001 in calculations and report 0.01 for reductions of our measure vaules, i.e. other distances. Area reverts to an evaluation of of the precision of the input and by convention most will hold to the nearest square foot and not round to the nearest 5, 10 or greater square feet. In turn when we reduce to acres, we report to 0.1, 0.01, 0.001 or 0.0001 depending on the size of the surveyed tract as well as our survey precision.
Paul in PA
Butch
Like this?
MULTIPLICATION AND DIVISION:
When multiplying or dividing numbers, count the NUMBER OF SIGNIFICANT FIGURES. The answer cannot CONTAIN MORE SIGNIFICANT FIGURES THAN THE NUMBER BEING MULTIPLIED OR DIVIDED with the LEAST NUMBER OF SIGNIFICANT FIGURES.
Example:
23.123123 (8 significant figures)
x 1.3344 (5 significant figures)
30.855495 (on calculator)
30.855 (rounded to 5 significant figures)
Quoted from:
http://www.usca.edu/chemistry/genchem/sigfig2.htm
Paul
See my reply to Butch.
BTW - rules for significant figures do not vary from profession to profession. They are a mathematical concept - whether you are dealing with acres, or liters or astronomical units is irrelevant.
Butch
> Like this?
>
>
> MULTIPLICATION AND DIVISION:
>
> When multiplying or dividing numbers, count the NUMBER OF SIGNIFICANT FIGURES. The answer cannot CONTAIN MORE SIGNIFICANT FIGURES THAN THE NUMBER BEING MULTIPLIED OR DIVIDED with the LEAST NUMBER OF SIGNIFICANT FIGURES.
>
Jim, how many sig figs does 1.9 have? Now, how can you say the answer is 1039.9 which has 5 sig figs?
edit: it should be clarified to state measured values/numbers. If a number is a defined or named value, like say an easement strip that must be limited to 2', then it can presumed to have an infinite # of sig figs, and not just limit a calculation to 1 sig digit.
Significant Digits Rules Apply To Like Numbers
547.34 and 1.9 are no where near alike.
Consider 544.5 * 1.91, they are much more alike.
The result of my example is 1039.995 or 1040.0 or better yet 1040.
Pay attention that adding that 0.01 to the small value changes what is needed in the larger value by almost 3 units.
Paul in PA
Significant Digits
547.34 x 1.9 = 1039.946.
The number of significant figures tells you the uncertainty in each.
So, the lowest possible area would be 547.33 x 1.8 = 985.19.
The highest possible area would be 547.35 x 2.0 = 1094.70.
Without having to get too deeply into statistical theory, it would be expected that the area is somewhere within this range. It is less likely that both will be off by the maximum amount of uncertainty.
Using the approximate average of these two would not be unreasonable....so say 1040, plus or minus.
Significant Digits
Adding to what Angelo said.
547.335 * 1.85 = 1012.57
547.345 * 1.95 = 1067.32
= 1040 +/- 27 or +/- 25 or +/- 30 depending on how you look at it.
but 1040, whole digits and conveniently to the nearest 10 is the best you can get.
Paul in PA
Significant Digits
Why don't you use these bounds?
547.335 x 1.85 = 1012.579
547.345 x 1.95 = 1067.323
Still resulting in 1040 as the reported number.
This example again points out one of the biggest flaws in the whole scheme - the least digit in a number beginning with a 10 is not worth as much as that digit in a number beginning with 9.
Why'd you change your mind? I liked 1.1 x 10^3 much better. 1,100 is probably okay, too, since the zeros should not be considered significant.
Butch
I can't beleive there is even debate about this, it's not an opinion question and the rules of sig. figs. are pretty easy to understand. I think Jim is confusing the rules for adding vs. multiplying and thinking the answer should be to the tenths place because 1.9 is to the tenths place...
> Why'd you change your mind? I liked 1.1 x 10^3 much better. 1,100 is probably okay, too, since the zeros should not be considered significant.
Stephen changed the numbers that he was multiplying, so the answer changed, also. :>
That is, the first thread asked:
574.34' * 1.9' = ?
and the second:
547.34' * 1.9' = ?
Good catch ... I completely missed that the numbers changed. Wouldn't 1.0 X 10^3 be the best answer for that one?
Significant Digits
#1 OK, guys, I had several categories unchecked in my profile that was preventing me from seeing the posts once I navigated away from the site. Now that's fixed thanks to a helpful email from Kent.
#2 This is an academic question. ACADEMIC. The first question was:
574.34' * 1.9' = 1,091.246' which according to the rules of Significant Digits, should be rounded to 1,100'. This seems fair and appropriate.
The second question concerns switching two of the digits as in:
547.34' * 1.9' = 1039.946'. By the rule of Significant Digits we have to constrain the answer to two digits. Is the answer...
1,040'? No. Three sign. digits.
1,000'? No. One sign. digit.
1,100'? Well, I guess, it has the right number of digits (Two), but, it seems odd to round up further for the correct answer than rounding down to 1,000'. And it seems odd that decreasing the quantity of the first number to be multiplied results in less precision in the result.
Butch, at least, seemed to get the point I was driving at, namely that following the rules of significant digits, which are UNIVERSAL rules (I didn't invent them, and they apply to any math calculations that involve approximate numbers), seems to lead to absurd results.
"Applying the rule of sig figs to survey computations doesn't always provide meaningful data." and
"If the lesser measure could have been stated to the hundreth, the uncertainty changes by an order of magnitude, making it (uncertainty) much less consequential."
#3 Talk like a bitch; get slapped like a bitch.
Stephen