# Significant figures | Decimals | Pre-Algebra | Khan Academy

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
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.

## 47 thoughts on “Significant figures | Decimals | Pre-Algebra | Khan Academy”

1. Injela _ Duh says:

1:58
It clicked
U saved my grades and my future
Thank u

2. Hifzhan says:

here for Maths

3. Danielle Brant says:

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

4. Fillia A says:

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

5. Seven Gagate says:

2018???

6. sara says:

You should do upper and lower bounds

7. Zanah Taha says:

sorry, what?

8. Zanah Taha says:

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.

9. Zanah Taha says:

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

10. Bhargav Guntupalli says:

I love u khan.

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

11. varun nair says:

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

12. navyblueshawl says:

WHY 370 IS 3 significant but 37000 is 2 sf?

13. dope chocolate says:

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

14. CateIsMyName says:

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

15. Delta Media - Brawl Stars & More! says:

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.

16. LEE SHIN HUI - says:

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…

18. DigitalDavinci says:

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

19. Joseph Jesse says:

Sig fig

20. Daniel Steinke-Lucas says:

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

21. Career Channel Pak says:

SIR WHICH SOFTWARE YOU USED FOR LECTURES WRITING

22. Lewis Hoang Long says:

I came here for chem theory

23. Anonymous Python says:

0.10 -> 2sf
0.001-> 1sf
10->1sf
10.0->3sf
10.0001->6sf
Is this right i have no idea

24. Finn Smith says:

this is truly epic

25. Alexxzzz _ 246 says:

anyone here in 2019

26. neil singh says:

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

27. Sami Al Taie says:

He sounds like the Rock.

28. Danial Ismael says:

Thanks that worked

29. Plastic Spoon says:

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

30. Bhumika Sahu says:

Still confused….lol🤔😒

31. frh neil says:

now it makes sense a lil bit

32. Viktor Iartav says:

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

33. George Herron says:

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

34. Jelly_belly101 _ says:

I kinda get it

35. Steven Copeland says:

Am I the only one who actually understands this?

36. Luke Fasanello says:

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

37. Jackson Miller says:

Brian Grant from mcoc narrating?

38. FoxoutTV is good says:

how he write a words by mouse?

39. Ch Ed says:

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

40. Soda Kim says:

I am here cause I have an exam tomorrow on Math :))
Thanks from the video :))

41. 23Haylee Markijohn says:

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

42. HYPER GAMING says:

43. Mark Bacon says:

Anyone here for Kinesiology?

44. Ryan Plays says:

its math

45. Basil Tom says: