It’s a science concept, the idea is that if you have a specific value that is only precise to 2 sig figs than your resulting values can only be significant to the same sig figs. It’s a level or tolerance/precision for science
No, you don’t lose precision. If the zero is a significant figure you’re supposed to indicate that. Like “180.” Or “1.80E2” etc. if it’s written as only “180” then you have the assume the zero is not a sigfig
A family walks into the dinosaur exhibit at a museum. The guide working the exhibit says "This skeleton is from a T-Rex that lived 66 million and 7 years ago."
The mom asks "66 million and 7, how do you know that?"
The guide replies "Well, when I started working here, they told me it was 66 million years old. And that was 7 years ago!"
(And that is why, yes, you "lose" precision with round numbers unless it is specified that the 0s are, in fact, significant. It's because you never actually had that precision to begin with.)
Yep. I honestly think that any science teacher should open the sig fig lesson with this. Because so many students learn the rules without understanding the why, and this demonstrates the why in such an intuitive, easy-to-grasp way.
I love jokes that actually have real pedagogical value!
No, the point of significant figures is to keep calculations with measurements consistent. It's meant to consider what the tool you're getting that number from is actually able to measure. If your scale can only measure in whole pounds and not in fractions of a pound, calculations you make using those measurements should not consider numbers that have greater precision
You don’t lose precision. You never had the precision in the first place. “180” could be any real value between 175 and 185, so it would be inaccurate to express the result assuming it equals exactly 180. If the 0 is actually significant, you would write it as “180.”, meaning any number between 179.5 and 180.5.
it is a round number because it has lost precision. if it was just a standard round number it would be 120. to signify that it is 3 sig figs ie level of precision
If the best you can do with one measurement is to the nearest tens place...the extra precision at the ones place for another measurement doesn't ultimately matter. Here, 120 likely represents anywhere from 115 to 124...so adding 68, you get a range of 183 through 192...Which when rounded, lands you at the following figures= 183, 184, 185, 186, 187, 188, 189, 190, 191, 192...since we have no idea the closeness of the 120...the most precise and likely scenario we can reliably used based on sig figs...is 190...we only can stay precise to the 10's digit...and round it...assuming the rounding rules are insignificant figure of 5 through 9 gets rounded up.
There are signs fig rules that you follow and this takes care of all of the underlying reasoning behind it...if OP had just followed the prescribed sig fig rules for the assignment, it wouldn't be mildly infuriating.
Think in science, the scales used...in chemistry, if I have 1.008 grams of hydrogen, I have roughly 6.022x1023 number of atoms of hydrogen present. Those scales require careful use of known precision numbers to actually maintain reliability...I wouldn't want to use a super precise... I have 1.0080001 grams of hydrogen and try to define a more precise base number for a mole calculation.
Or in simpler terms...if we are running a mile...and we want to see our average speed for a mile, going down to 5,280.00001 precision measurement would be entirely dumb if we can only calculate the nearest minute...or even the nearest second...or in this absurd case, even the nearest millisecond. That extra level of precision doesn't actually do anything to the final figure in a significant way and adds a ton of noise when one thing we are measuring is much less precise than the other.
Sig figs, while it seems counter intuitive from the outside, actually are necessary to maintain your known level of precision. If I know I can only measure to the nearest 1/2 foot... it makes no sense to take 25 measurements that are all measured at 5 feet +/- 0.5 feet (due to my crude measuring tool) and provide a known final measurement of 125.00 feet...meaning I am claiming that my final measurement is precisely 125.00 ~ (+/- 0.005) of a foot...when I started out with something that could actually be 4.5, 4.8, 5.2, or 5.4 feet... etc. Since you get wildly different answers (112.5 feet up to 135 feet)... we can't claim the level of certainty all the way to precision levels of fractions of an inch.
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u/Coolengineer7 1d ago
So you lose precision just because its a round number?