Significant Digits

Mr. Andersen explains significant digits and shows you how to use them in calculations.
Intro Music Atribution
Title: I4dsong_loop_main.wav
Artist: CosmicD
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[@samirgunic]

I summery, you may think of it this way. When you do the operation of adding and subtracting numbers, you already have the accuracy and you only adjust the result for the precision so that it doesn't look more precise than it is. When you do the operation of multiplying or dividing numbers, you are changing the accuracy so you need to adjust the result by looking at the number of sig figs so that the result doesn't appear more accurate than it is.

[@10booleee]

This helped me so much in Pre-AP Chem! Thank you! Oh, and last year you helped me finish the year with a 99 in Biology. :)

[@Felipe-53]

Awesome video, as always. Thank you!

[@matiasgreene8437]

My chem teacher always gives me the easiest shit for HW but the hardest stuff during the test

[@pamelaortiz1395]

I really enjoyed The Scientific Method segment. I'm beginning my journey in to the science field and your link was given to me by my Professor. I look forward to viewing many more of your segments

[@j3226]

So it wasn't just me that caught that error with 230. having three significant figures.

[@ther3sz]

ughhh, my chem teacher brought me here

[@celus3101]

ugh !

[@womp9465]

same boat as you guys :/

[@Melissa-sh9ff]

Same😔

[@randomnessunite]

ayyy same

[@ndukauguna9847]

Physics teacher

[@RaquelDubs]

Thank you. I didn't fully understand sig digs but thanks to you now I do!

[@198rabia]

Superb. Your videos really teach me. Thanks

[@cxperez]

Really enjoyed this!

[@ssymck]

you are so great! thx from germany!

[@luisyebra1722]

I like pancakes

[@amanir4502]

PLEASE PLEASE do the regular chemistry videos too, it would really help me with AP Chemistry. Thanks^^

[@juliengrigaux3736]

Ms yu!!!!!

[@squilliamfancison693]

Oh yeah!!!

[@marthamaldonado5353]

Who else is here because of AP bio?

[@ArcticJS]

AP earth science for me lol

[@aiyanalam5784]

Biotech class! We need to know this stuff!

[@brendenbrown7666]

8th grade

[@r3g3nl]

How is the final calculation of an exponential function defined by significant figures?

[@sethpeace9235]

1:40 isn't the wasp 1.5 cm since the ruler starts at 1 not zero?

[@samirgunic]

For example! You can say that 7350 is precise to the nearest 10s place. Not 10THs! But 10s place! It's ambiguous because of the 0 at the end. But that only speaks for the accuracy. The precision is still there. You can't tell if this is a measure of exactly 7350 meters or something. Because you don't know if it was rounded or not. But if it was rounded it could only have been 7345 and rounded up, or 7354 and rounded down.

[@gabbyherrera3140]

bless you child

[@saifkhattab7039]

we need more examples on the sig figs with the scientific notation form

[@joshmonroe6285]

You never write digits in scientific notation that are not significant, so with scientific notation, you just count the digits that are there except the ten and it exponent.

[@samirgunic]

So you can assume that it is precis to the nearest 10s place, or at most to the nearest 100s place. So when you add 7350 + 54 = 7404 you can round the result to the same level of precision as the number that was least precise. Of these two I think that 7350 is least precise. The 7350 is precise to the nearest 100s place and the 54 is precise to the 10s place I think. Therefore, the 54 is more precise than 7350.

[@samirgunic]

It's similar with whole numbers. If you add 7350 to 54 you get 7404. But if you are adding 7350+54=7404 you don't care about sig figs. Just look at the decimal places. Right! There are no decimal points here. But this is still the decimal system! It doesn't matter if there is no decimal point or decimal comma. You can still have a precision. You don't have accuracy, but you do have precision. You just need to consider lower and upper bounds of the numbers.

[@AndyDaxter]

Nice video. However, what does having more digits ( more precise) has anything to do with having better reproducible result?

[@chrisashmore-good9815]

I had the same question. Wouldn't more tick marks on the measuring device make it more accurate? Better precision depends on the user, doesn't it?

[@hieuddo5752]

can someone explain for me the decimal point in the end of a number? for example :19,000. and 19,000 what is the different here?

[@samlee4996]

+Đức Hiếu Đỗ two significant digits

[@brandylutkins8035]

Five rules govern significant figures: 1. Non-zero digits are always significant; 1.121 has four significant digits. 2. Any zeros between two significant digits are significant; 1.08701 has six significant digits. 3. Zeros before the decimal point are placeholders and not significant; in the number .00254, only the 2,5 and 4 are significant, meaning the number has 3 significant figures. 4. Zeros after the decimal point and after figures are significant; in the number 0.2540, the 2, 4, 5 and last 0 are significant. 5. Exponential digits in scientific notation are not significant; 1.12x106 has three significant digits, 1, 1, and 2.

[@samirgunic]

Nice presentation! But what about whole numbers? Like 7350 + 54. Is this 7404 or is it 7400? And what about 7350 + 5400? Is this 12750 or 12800? Do you ignore this rule if the numbers are ambiguous (trailing zeros with no decimal point)?

[@elijahhohoho3013]

why is the end 0's important? like with 1.60 there's 3 significant digits, there's 5 significant digits with 1.6000, same number though ?

[@camerondavid8089]

Because 0 is still a number! 1.6000 is a big difference from 1.6444 in many aspects of science!

[@jasonsmith5313]

1.6000 was measured with a much more precise instrument than the one measured as 1.60

[@samirgunic]

When you want accuracy you look at number of significant figures, right? And when you want precision you look at the number of decimal places, right? For example, consider 6.07+122.245. The first one has 3 sig figs but is only precise to the 2 decimal place. The other one has 6 sig figs but is precise to 3 decimal places. The answer is 128.315 so you round it to 128.32. So the rule of precision should apply to whole number as well. I will look at it later on and give you an example.

[@xodus1386]

Sup Mrs. Kirby’s chem class 😔

[@alexsobotie9805]

Only thing missed is the value of 'exact' Numbers which have infinite number of significant figures and are therefore not considered in calculations.

[@vaneetgupta7189]

what about 0.0 ?

[@Gameplayery]

5:40 how is that 0 not significant ? there's a big difference between 230 and 23 !

[@TheWNDProject]

in represents a space when a 'ones" unit would be simply holding the empty spot making it 230 no 23

[@charlienguyen448]

+Rasti Al I agree with you. The way I was taught depends on if there is a decimal. For '230.', there would be 3 sf's, and for '230', there would be 2. The one in the video, since there is a decimal, has 3 sf's.

[@sahar1usa]

the multiplication asnwer should be 32 * 10 3

[@samirgunic]

Just a recap of what I wrote earlier. I was adding 6.07 to 122.245 which is 128.315 and then rounded it up to 128.32. Why? Because the smallest number of decimal places is 2! The number 6.07 has 2 decimal places but 3 sig figs. So I round my result to 2 decimal places. I don't care for sig figs here. If you care for sig figs you would round the result to 128 only.

[@Jai-jn7te]

4:32 *zeros

[@bertblankenstein3738]

So 14 x 1 = 10? And 10 x 1 = 1e1... I get the basics but feel that the trailing 0s could be significant. Also one must consider the accuracy of numbers. Example of doubling, can we take the 2 to have infinite significant digits, and the other number at its usual number of significant digits? To blindly apply rules doesn't make much sense imo.

[@kingbooger3032]

SIXTY NINE

[@JM-fo1te]

Forgot the units on the last problem.

[@paulperkins1913]

Me too

[@michaelperez3792]

what about 100400km

[@keshawilliams2976]

4 sig fig

[@samirgunic]

This has nothing to do with accuracy and sig figs! These are different concepts - precision and accuracy. This all boils down to rounding results when doing calculations. Different rules apply to addtition-subtraction and to multiplication-division.

[@justinmayeshiro7600]

Booyahkasha

[@patrickh9268]

Actually the answer is .759 m/s

[@logandevack1800]

even more so, it would be even more scientifically accurate to put 0.759 m/s

[@TheOriginalArchivist]

@@logandevack1800 No that isn't more "scientifically accurate" the 0 is leading, so it is not significant. 00000000000000.759 is equally valid as 0.759 or .759

[@saeghe2000]

230. has 3 significant figures not 2

[@jestoni1998]

True

[@abinaya276]

jestoni1998 It has two significant figures. Zeros in non-decimal numbers are insignificant. 2 and 3 are the only significant digits.

[@remavas5470]

+Abinaya Kalpathi there's an extra dot to signify it was accuratly measured to the unit's digir

[@augurelite]

Ooooooooh

[@itstimetohajima9524]

oi dmc kids

[@hopetutorstexas]

Please address exact numbers. Your video is being used to teach the concept of sig. figs. by a physics teacher who thinks that 3 oranges at 4.23 grams each means there is only one sig. fig, and thus the answer is 10. Her students are all failing because this goes against all known practice and logic. Thanks.

[@truedominator13]

at 5:48 you can see 69

[@SinhaleseDravadia]

Why do you need this crap significant digits in Chemostry

[@garrettwest8294]

what about 0.0?