# Significant figures in 0

1. Feb 13, 2006

### Mattara

I've been pondering over this question for quite some time. How many significant figures are there in 0?

Is 0 really 0 and therefore doesn't have any significant figures at all just becuase of the fact that it is 0 and is by definition nothing at all?

Or does the number 0 have one significant figure because if the number 0 is added to a line of numbers:

it appears to have 1 siginificant figure.

And does it depend on where the 0 is found. If it is on an absolute scale where 0 truly means nothing (ex. Shelly ha`s 0 apples) or in the middle of a scale (ex. 0 degrees C)?

Last edited: Feb 13, 2006
2. Feb 13, 2006

### HallsofIvy

Staff Emeritus
There are no significant figures in any "number"- there are significant figures in measurements. If you measure something with a measuring device that is accurate to 0.005 of whatever units are appropriate then you have 3 significant figures in the result. In particular, if you measured a value of 0 +/- 0.005 then you would write
0.00 meaning that it could be as low as -0.005 or as high as 0.005. If you could only measure to with 0.05 you would write 0.0. The significant figures depend upon your measuring equipment and the way you write the numerals, not on the numbers themselves.

3. Feb 13, 2006

### Mattara

ok, guess i wasn't clear enough.

Let's say i measure the current temerpature to be 0 degees C (with no decimals = not überaccurate termometer). How many significant figures are there in that measurement? And how would that differ from the measure 0 K with the same termometer? (it cant' be done of course but what if?)

4. Feb 13, 2006

### krab

So.... this is not a mathematics question. In engineering, if you are using a thermometer that is accurate to 0.01 degree, and you measure zero within measurement limits, then the result is quoted as 0.00 degrees. The trailing zeroes are used to emphasize the known accuracy of the measurement.

5. Feb 13, 2006

### Mattara

Yes it is, since the original idea has to do with math

6. Feb 13, 2006

### HallsofIvy

Staff Emeritus
I don't see a whole lot of math. If you assert "Let's say i measure the current temerpature to be 0 degees C " then there is exactly one significant figure- you only have one figure.

"And how would that differ from the measure 0 K with the same termometer?"
A great deal! 0 K is one hell of a lot colder than 0 C. If you are asking specifically about the the significant digits then I can only say that in each of those measurements there is one significant digit because you said so- you only wrote one digit. Of course, I have to assume that YOU know the accuracy of your thermometer and writing the digits to show that. If you have a thermometer that measures to the nearest tenth of a degree then you should write 0.0 degrees.

7. Feb 13, 2006

### Mk

His thermometer is accurate to the degree. i.e. 1K, 300K, 23K. If you are using a thermometer to measure this, and you get 0 degrees, that would be no significant digits.

0 K, is about 273.15 degrees C colder than 0 C.

8. Feb 14, 2006

### Nacho

There's two terms being used here: significant figures and significant digits. I personally have never heard of or used the term significant figures .. not to mean that it isn't ever used ..

But significant digits is usually used with floating point calculations, and ignores any place value and uses/counts only the digits that are between left and right zeros as the number would be expressed in decimal form. Thus:

.000247

and

.0000024700000

would both have 3 significant digits.

Considering that with the original question, I can't figure out if a flat answer of "0" would have any significant digits or not.

Last edited: Feb 14, 2006
9. Feb 14, 2006

### Mattara

About the figures/digits thing. I'm from Sweden and i wasn't sure about the english terminology.

The temperature was only an example, I could have used anything. Was i meant was:

How many significant digits in a measurement of some sort that gives 0 (+- 1)which isn't the lowest term (ex. Celcius temperature) and how many significant digits there are in a measurement of some sort that gives 0 (+-1) which is the lowest term (ex. Kelvin temperature)

10. Feb 14, 2006

### Nacho

Is that not just a matter of precision, which I take is what the others were actually responding? The precision is arbitrary, and reflects only how accurate you can measure the temperature. In your example above, the precision would be +- 1 degree. Celsius and Kelvin use the same exact units, and would have the same expression of precision, the only difference is the scale is offset by a number of degrees.

If OTOH, if you are asking to what precision can 0 degrees Celsius be measured to, and to what precision can 0 degrees Kelvin be measured to ... I have no idea of that answer.

Last edited: Feb 14, 2006
11. Feb 14, 2006

### Integral

Staff Emeritus
Significant digits, significant figures.. its all the same. In physics they are part of any measurement and determined by the instrument used to make the measurement and the confidence/experience of the person making the measurement. You cannot meaningfully speak of significant figures without reference to the measurement and the methods used to obtain the measurement.

12. Feb 14, 2006

### Nacho

What I think of the difference, they are not necessarily the same in computations though.

For instance, in a lot of financial calculations errors will creap up through digits of precision, unless you take care to split the numbers up into a mantissa and exponent, and adapt the formula to use intermediate products. The significant digits of the mantissa, and scaling the exponent lead to a greater degree of precision for computer computations than straight repeated multiplying of a number with a fixed number of digits. There are aribtrary precision programs out there, but they can be quite slow.

I guess its all about using those terms in measurements VS computations. Physics uses both.

13. Feb 14, 2006

### Mk

Doesn't the second one have eight, because you have to count the ending zeros right of the decimal?

14. Feb 15, 2006

### Nacho

Mk,

Good point. I think there's good arguments for either .. If you chose 8, how could a person looking at the answer ever figure out computations were done on those rightmost 5 digits to arrive at a zero in that digit? I guess you could say because they were written that way ;) but also consider the same answer in scientific notation (floating point) stored in computer with a mantissa of 32 digits. There would be 29 right zeros with no indication computations were done on any of those digits.

15. Feb 15, 2006

### Mk

Well, if the value is a defined one, such as 299,792,458 m/s, it has an infinite number of zeros after the decimal, and therefore has an infinite number of significant digits.

16. Feb 15, 2006

### Mattara

.0000024700000

Correct me if I'm wrong but this number has either 3 or 4 or 5 or 6 or 7 or 8? Everyone of them is correct?

17. Feb 15, 2006

### bomba923

What's the confusion?? .0000024700000 has 8 significant figures.

If it helps, think of .0000024700000 as 2.4700000*10-6.

18. Feb 15, 2006

### Mattara

Yes it has 8 significants but also 7 or 6 or 5 or 4 or 3. Take your pick.

19. Feb 16, 2006

### cepheid

Staff Emeritus
Ummm....no. It has 8.

20. Feb 16, 2006

### Mattara

Not according to my physics book, teacher and test scores.

Or is it measurements like 100 that has 1 or 2 or 3 sig. dig.?

Last edited: Feb 16, 2006