Wikipedia:Reference desk/Archives/Mathematics/2009 August 21

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August 21

Quadratic turd

My friend tell me there is a number called "quadratic turd? Why is mathematicians so vulgar to call a number turd? 67.101.25.201 (talk) 01:28, 21 August 2009 (UTC)

Quadratic surd Black Carrot (talk) 04:34, 21 August 2009 (UTC)

"Surd" from Latin surdus meaning deaf or mute - see Jeff Miller's "Earliest Known Uses of Some of the Words of Mathematics". Gandalf61 (talk) 12:12, 21 August 2009 (UTC)

Significant digits

Does the fact that 304.52 has 5 significant figures while 4.52 has 3 mean that the former is any more accurate? DRosenbach ^{(Talk | Contribs)} 03:59, 21 August 2009 (UTC)

If they've been rounded, they're equally precise relative to a given unit of measure, and the first is more precise relative to its size. Significant digits is a loose measurement of precision relative to size. Black Carrot (talk) 04:35, 21 August 2009 (UTC)

Quite right, but precision and accuracy are not the same. Accuracy is closeness of a measurement to the "actual" value. Precision is how specific the measurement is i.e. how many digits after the decimal point are displayed. For instance, my computed value of pi at 9.7564648389271381932 isn't very accurate, but it's pretty precise by most standards!--Leon (talk) 11:23, 21 August 2009 (UTC)

But since they share the same number of post-decimal digits, I figure the former measurement expresses no greater precision. If I am measuring the lengths of two pieces of wire, it's merely a reflection of our 10-base scale that makes a length of 9 one significant figure but 10 two significant figures. I mean, let's say we had an 11 base system with the symbol ¿ serving to signify the number "one greater than 9" and "one less than 10." Is measuring with our new number system make my measurement any less accurate? At first blush, I reflect that the smaller one's scale, the more precise a measurement should be, because it's easier to think about one unit, half a unit, a third of a unit, a sixth of a unit, etc., and each of these successive fractions is a smaller measurement for a smaller scale unit. I'm going off on a tangent here with my philosophical queries (I suppose there are about 4 different topics I've touched on above) but my main issue in asking this question is why adding pre-decimal digits adds precision when there doesn't seem to be any greater specificity in my measurement...It's just that one runs out of equivalent number of digits in our counting system and one must therefor carry it over to the next space. I hope this makes sense. DRosenbach ^{(Talk | Contribs)} 13:28, 21 August 2009 (UTC)

The reasons you mention are part of why significant figures aren't used in serious work. They are only really used in schools. Actual scientists will specify the precision in ways that don't depend on what base you are writing the numbers in. For example, you could say "10 +/- 2". You can measure precision either absolutely ("+/- 5") or relatively ("+/- 5%"), which is more useful depends on what you are doing with the numbers. --Tango (talk) 13:41, 21 August 2009 (UTC)

Are you talking absolute accuracy or relative accuracy? As written, both have the same absolute errors: ±0.005 units. They differ in their relative precision, though. 4.52±0.005 has a 1100 part per million error, while 304.52±0.005 has a 16 ppm error. Another complication is if the two numbers are in different units: 4.52±0.005 light years has much larger errors in both absolute and relative terms than 304.52±0.005 km. -- 128.104.112.102 (talk) 16:00, 21 August 2009 (UTC)

Yes -- that distinction definitely answers my query. Wow...that was spectacular. Thank you! DRosenbach ^{(Talk | Contribs)} 02:12, 23 August 2009 (UTC)

Wait...could you explain the 1100 vs. 16 ppm portion, I didn't get that. DRosenbach ^{(Talk | Contribs)} 02:15, 23 August 2009 (UTC)

"ppm" essentially means ${\frac {1}{1000000}}$. A relative error of 1 ppm would mean that the error is a millionth of the actual value. In the 4.52±0.005 case, the relative error is

${\frac {0.005}{4.52}}\approx 0.0011={\frac {1100}{1000000}}=1100\mathrm {ppm} .$

-- Meni Rosenfeld (talk) 10:57, 23 August 2009 (UTC)

That much I understood -- my followup was more so directed at how the other calculation possesses a denominator of greater magnitude yet results in ppm of much lesser magnitude. Was it a typo? Forgive my temporary idiocy. Got it, thanx! DRosenbach ^{(Talk | Contribs)} 13:06, 23 August 2009 (UTC)