Let’s see if we can

learn a thing or two about significant

figures, sometimes called significant digits. And the idea behind

significant figures is just to make sure that

when you do a big computation and you have a bunch

of digits there, that you’re not

over-representing the amount of

precision that you had, that the result isn’t more

precise than the things that you actually measured, that

you used to get that result. Before we go into

the depths of it and how you use it

with computation, let’s just do a

bunch of examples of identifying

significant figures. Then we’ll try to come up

with some rules of thumb. But the general way to think

about it is, which digits are really giving me

information about how precise my measurement is? So on this first

thing right over here, the significant figures

are this 7, 0, 0. So over here, you have

three significant figures. And it might make you a little

uncomfortable that we’re not including these 0’s that

are after the decimal point and before this 7, that

we’re not including those. Because you’re just like, that

does help define the number. And that is true, but

it’s not telling us how precise our measurement is. And to try to understand

this a little bit better, imagine if this right over

here was a measurement of kilometers, so if we

measured 0.00700 kilometers. This would be the exact

same thing as 7.00 meters. Maybe, in fact, we just

used a meter stick. And we said it’s

exactly 7.00 meters. So we measured to the

nearest centimeter. And we just felt like

writing it in kilometers. These two numbers are

the exact same thing. They’re just different units. But I think when

you look over here, it makes a lot more

sense why you only have three significant figures. These 0’s are just

shifting it based on the units of measurement

that you’re using. But the numbers that are

really giving you the precision are the 7, the 0, and the 0. And the reason why we’re

counting these trailing 0’s is that whoever wrote this number

didn’t have to write them down. They wrote them down

to explicitly say, look, I measured this far. If they didn’t

measure this far, they would have just

left these 0’s off. And they would have just

told you 7 meters, not 7.00. Let’s do the next one. So based on the same idea,

we have the 5 and the 2. The non-zero digits are going

to be significant figures. You don’t include

this leading 0, by the same logic that if

this was 0.052 kilometers, this would be the same thing as

52 meters, which clearly only has two significant figures. So you don’t want

to count leading 0’s before the first non-zero

digit, I guess we could say. You don’t want to include those. You just want to include all the

non-zero digits and everything in between, and trailing 0’s

if a decimal point is involved. I’ll make those ideas a

little bit more formal. So over here, the

person did 370. And then they wrote

the decimal point. If they didn’t write

the decimal point, it would be a little unclear

on how precise this was. But because they wrote

the decimal point, it means that they measured

it exactly to be 370. They didn’t get 372

and then round down. Or they didn’t have

kind of a roughness only to the nearest tens place. This decimal tells you that all

three of these are significant. So this is three significant

figures over here. Then on this next one,

once again, this decimal tells us that not only did

we get to the nearest one, but then we put another

trailing 0 here, which means we got

to the nearest tenth. So in this situation,

once again, we have three

significant figures. Over here, the 7

is in the hundreds. But the measurement

went all the way down to the thousandths place. And even though there

are 0’s in between, those 0’s are part

of our measurement, because they are in

between non-zero digits. So in this situation,

every digit here, the way it’s written,

is a significant digit. So you have six

significant digits. Now, this last one is ambiguous. The 37,000– it’s

not clear whether you measured exactly 37,000. Maybe you measured

to the nearest one, and you got an exact number. You got exactly 37,000. Or maybe you only measured

to the nearest thousand. So there’s a little

bit of ambiguity here. If you just see something

written exactly like this, you would probably say, if you

had to guess– or not guess. If there wasn’t any

more information, you would say that there’s

just two significant figures or significant digits. For this person to

be less ambiguous, they would want to put a

decimal point right over there. And that lets you know

that this is actually five digits of precision,

that we actually go to five significant figures. So if you don’t see that decimal

point, I would go with two.

1:58

It clicked

U saved my grades and my future

Thank u

here for Maths

Could the 10.0 number have 1 significant figure instead of 3 significant figures?

I have a test in 3 hours and thats why im here, thank you Khan XD

2018???

You should do upper and lower bounds

sorry, what?

first khan academy video I don't understand. I've been watching these videos forever, and this is the first one I just don't get. I am confusion.

sig figs are petty zeros that are saying I matter too bihh

I love u khan.

My teacher said test guys and dint teach us dung beetle stew

In that case even 10 has only one sig fig as 10mm =1cm so if converted to cm it has only 1 sig fig.

WHY 370 IS 3 significant but 37000 is 2 sf?

this is probably my 27th time watching this topic/vid

Im here for physics and chemistry 😭😭😭 my final exam in physics later 😂

I Bet there is something else about significant figures in engineering science, Im actually confused on how it even works right..

I asked my teacher and else but he explained and Im still experiencing different type of sig figures here.. Hes wrong? or there is just different type of significant figure system in engineering… I mean in the last example I understand more! Hopefully, it all goes ok.

The explanation in this vid is so detailed, my teacher taught me this for frst chp in mod maths , n i was so confused like why is the zeroes bf non-zero digits are not significant, n he said , bcs its like that , no explanation, i was so befuddled n was very glad i found this vid, it gave me the explanation i needed ! Thankyou so much!

A bit confusing…

Lost 30% on an assignment because of these, even though all my answers were technically correct.

Sig figAt 2:37, that's how I sound when I try to explain stuff all the time LOL

SIR WHICH SOFTWARE YOU USED FOR LECTURES WRITING

I came here for chem theory

0.10 -> 2sf

0.001-> 1sf

10->1sf

10.0->3sf

10.0001->6sf

Is this right i have no idea

this is truly epic

anyone here in 2019

DOUBT:

In the first example of 0.00700 km instead of converting it into metres we could also convert it to 700 cms which only has 1 SIGNIFICANT DIGIT as compared to 3 in 7.00m

He sounds like the Rock.

Thanks that worked

You explained it better in 5 mins than my teacher did in one hour…..

Still confused….lol🤔😒

now it makes sense a lil bit

I am doing electrical engineering. And I'm here too. XD

about to enter 9th accel chem/phys and just figured out that sig means significant figures

I kinda get it

Am I the only one who actually understands this?

I've taken 3 chemistry classes and 2 physics classes, I've had to watch this video 5 times now

Brian Grant from mcoc narrating?

how he write a words by mouse?

Do people study these in grade 7? Cos I do…

I am here cause I have an exam tomorrow on Math :))

Thanks from the video :))

Everyone is talking about chemistry and physics but I'm learning this in 9th grade physical science in highschool

PLEASE APNA CHANNEL BAND KAR

Anyone here for Kinesiology?

its math

i love your voice

Does a monetary symbol make the valid qualification for the zero to be significant?

Thanks man this help me a lot