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I'm currently in a Chemistry class, and one of the things we've learned is rounding numbers to the correct numbers of significant figures. It's easy stuff, so it's not troubling me, but I've just been wondering what the point is in rounding to significant figures. Is there any practical use for it, or did some scientist or whatever one day decide we should do that?

2007-09-14 17:22:16 · 5 answers · asked by chucknorris=theman 2 in Science & Mathematics Mathematics

Why would it be so important that an answer could be wrong, just because it has one more digit, etc.

For example, I would've gotten a perfect grade on a quiz if i had put 50.mL instead of 50 mL (the correct answer had a decimal after the 0). It didn't upset me though, I found it kinda funny actually.

2007-09-14 17:42:08 · update #1

5 answers

The use of significant figures is about precision and accuracy of the instrument you are using.

If you measured a ball with a pair of calipers vs a meter stick, the calipers would by far be more precise, so you would indicate this with the right amount of decimal places.

Let's say that you were measuring something with an instrument calibrated to the nearest millimeter. The item you measured lies just under the next centimeter mark. If it they measured 1.23 meters, you would record this as 1.2300. This doesn't change the magnitude of the measurement but indicates how accurate you are.

1.23 meters says that you measured 1.23 meters + or - 4 centimeters.

Whereas 1.2300 meters would indicate + or - 4 millimeters.
This measurement is more accurate.

However, for any computation you will round down the least accurate measurement.

EDIT:

In your example, the number 50mL is ambiguous or has a trailing zero. It could be 1 or 2 sig figs. It does not indicate the accuracy of the measurement. You're not saying what numbers are significant. 50. mL indicates that everything to the left of the decimal is significant. If in doubt, the proper notation would probably be 5.0 x 10^1 mL or 5.0 E1 mL

2007-09-14 17:40:04 · answer #1 · answered by ? 3 · 0 0

There is a famous example. When Mt. Everest was first measured back in Victoria's time, it was done by triangulation surveys from the Indian Ocean and was done so carefully the surveyors were sure it was done to the nearest foot. But when they did the calculations, they got 29,000 feet. While in a scientific paper, they would say 2.9000x10^4 and the would tell everyone the accuracy and how many significant digits, according to the story, they were concerned that people seeing 25,000 in the popular press, it would look like they had sort of guessed to the nearest ten or 100 feet, so, supposedly, they sat around the fire in northern India and first thought of saying it was 25,001, but that looked flakey. They couldn't make the queen's mountain shorter, so 28999 was out of the question. So they offered up 29,002 feet and reported that as showing the accuracy they had worked at.
The practical use is that when doing calculations, it is very easy, with division especially, to have a calculator come out with lots of decimals. If I measure 12 inches with a ruler and am told to report it in yards, it becomes 1/3 or 0.3333333333.... but the last number is absurd. If I carefully measured with a common ruler, I might be able to claim reading it to 12.2 or even 12.25 inches, so if it was exacly a foot, I might report 12.0 or 12.00. Reporting that it was anything other than 0.333 or 0.3333 yards would be adding far to many significant digits and might throw everything else off.
One other practical place that has consequences is calculating interest. If the interest rate is 4.125 (four and one eighth), then if 6 people have deposits totaling $1,000 the interest to be paid out is $41.25. But if one person has 133.33 on deposit, shall he be paid 0.04125*133.33 = 5.4998625? No, because we calculate money to only two decimal places. He would be paid $5.50. But where does the money come from to do this - by rounding other people down. But what happens if everybody keeps their balance so they all round up (or down)? One of two things: a crooked programming moves any extra pennies to his account (this actually happened) or the rounding point is moved, say from 0.50 to 0.51 or 0.52 so the same number of pennies are needed for rounding up as are taken in rounding down.

2007-09-15 01:07:04 · answer #2 · answered by Mike1942f 7 · 0 0

Many times, when dividing fractions and whole numbers into fractions, you can get lengthy or even irrational numbers. It's a waste of time to type 3.14159265357 into a calculator, for example, when all those extra digits behind the decimal point have little effect. Rounding to significant digits makes it a manageable number that gives you what you need without too much information. Yes, in mathematics, you can have WAY too much information.

Some numbers have undefined amounts of digits behind the decimal place. In those cases, rounding is the ONLY option.

Also, what was said above is important. If you have answers that resolve to only, say, one place behind the decimal, you shouldn't have an answer that's ridiculously long and deceptively "accurate." It's misleading.

2007-09-15 00:29:07 · answer #3 · answered by Big Will 2 · 0 0

There is a simple reason. If you perform some calculation, you can't know something to a greater degree of precision than the least precision of all the variables you used to perform the calculation. For instance, think of a simple physics formula: Force = Mass X Acceleration. If you measure the mass to the 1/100th of a kilogram and the acceleration to the 1/100th of a m/s^2, then, regardless of the calculation of the formula, you can't predict the Force to any precision greater than 1/100th of a Newton (kg * m / s^2). It is not an easy concept to grasp, but an important one in science.

2007-09-15 00:33:05 · answer #4 · answered by gitter1226 5 · 0 0

I'm glad it is easy for you, but I'm surprised noone has told you WHY it is done. Basically, a result should be no more precise than the least precise datum that goes into the result's formulation.

2007-09-15 00:28:16 · answer #5 · answered by cattbarf 7 · 1 0

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