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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 6

Lesson 14: Significant figures# Intro to significant figures

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers. Created by Sal Khan.

## Want to join the conversation?

- Can anyone help me because I got more confused watching the video...(26 votes)
- All non-zero digits are significant; 1, 2, 3, 4, 5, 6, 7, 8, and 9;

Zeros between non-zero digits are significant, like 705 and 80008;

Leading zeros are never significant, like in 0.03 or 0068;

Trailing zeros are significant ONLY if a decimal place is present; examples where the zeros are not significant include 100, 380; those that are include 38.00, 590.0, and 280.190;

I hope this helps!*Realizes that the post was made 8 years ago*Oh well(159 votes)

- What if the number is 0? Would that just be 0 significant figures?(23 votes)
- No. Alone zero is not considered as significant figure.(8 votes)

- At3:06, Sal covers the number 370. and how many significant figures there are in it. I'm confused about why someone would put a decimal after a number and not put any numbers after it. What is the purpose of this? If the measurement is exactly 370 anyway, why can't the number be 370.0 instead?(11 votes)
- From what I understand, '370.' shows that the number is accurate up to the ones place (e.g. that it is 370 and not a rounded 373 or 368). It could actually represent 370.4, but '370.' is still a correct representation of 370.4 as '370.'is accurate up to the ones place and 370.4 rounded to the ones place is 370.

370 and 370.0 mathematically represent the same number but with significant figures, 370 is accurate up to the ones place and 370.0 is accurate up to the tenths place. Referencing the previously mentioned example, 370.4 can be accurately represented as '370.', but not 370.0.

Hope that helps!(5 votes)

- I don't really get it is it just like : 00.30000 mean it's has 4 significant figures?(9 votes)
- 00.30000 has five significant figures: the 3 and the four zeros behind(12 votes)

- Why are the trailing zeros in a decimal number significant?(7 votes)
- Because they indicate that you measured that value to a higher degree of precision. If I measure something as exactly 100 millimeters and record it as 0.100 meters, that represents something different than saying 0.1 meters since in the later case it may of actually been 0.12m or 0.9m and I just rounded it off. By adding the extra 0s you know that the only rounding would have been to the nearest mm.(14 votes)

- If we have a number like 14.03 and we need to round it to one significant digit, how would we do this?(5 votes)
- Anthony is incorrect. If you want one significant digit, then the 4 is not significant either, and you just write down "10".(20 votes)

- i thought all digits were significant....

Protest for the rights of 0's!(8 votes) - How would we do this for a number like .3 repeating? Is the number of significant digits infinite?(2 votes)
- In the case of 0.3 repeating, then
**yes**, the number of significant figures is infinite.(4 votes)

- So basically.... the numbers that are not 0 AFTER the 0 will be counted as significant EVEN if there are more 0's after it?(3 votes)
- Perhaps someone has already mentioned this, but I don't have time to read all these posts, so if I've been redundant...my apologies. Anyway, some have tried to argue that 0.00 has three significant figures because to write it using scientific notation, you would need three zeros (0.00 × 10^1). However, from what I understand, writing a number using scientific notation requires the first factor to be a number greater than or equal to one, which would seem to indicate you NEVER use zero. I still contend that 0.00 has three significant digits though, but only because placing a decimal point AFTER a zero indicates that the zero is significant, and placing zeros at the END of a decimal number indicates they were MEASURED or else they would have been omitted. Yeah!(2 votes)

- I have a hard time getting what is significant and what isn't... Like, it's hard for me to grasp the concept of what MAKES a sig-fig, a significant figure.. Can someone explain it to me like I'm five years old?(3 votes)

## Video transcript

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.