# How many significant digits in 0 and 0.0?

1. Aug 27, 2009

### Bohrok

1. The problem statement, all variables and given/known data

I was helping some chemistry student and there was a homework problem on converting Fahrenheit to Celsius. The first two were 16°F and 16.0°F which were easy, but the last one was 0.0°F which had me wondering about 0 and 0.0.

2. Relevant equations

C° = 5/9(°F - 32) or C° = 1.8(°F - 32), but no trouble with actually calculating the answer.

3. The attempt at a solution

The problem was with the subtraction 0.0 - 32 (assuming 32°F has an infinite number of significant digits)
0.0
-32.0
-32.0

My thought was that the last 0 in 0.0 is significant even though there's no other nonzero digit to determine whether that last 0 is significant, since the first one is usually placed there by convention. Assuming the last 0 is significant, our answer was -17.8° which I'm sure is right in any case.

After thinking about what was significant in 0.0, I thought about 0.01 which has only one sig fig and the last 0 is just a placeholder, which led to thinking that the last 0 in 0.0 is not significant.

I looked at my edition of the student's textbook for similar problems and see one with converting 0°F to C°. The answer in the back said -18°C which is what I would get with 0°F having just one sig fig. Now, would putting a .0 on the end to make 0.0 make two sig figs?
How should a person look at these numbers?

2. Aug 27, 2009

### symbolipoint

You have two significant figures when your calculation is finished. Unfortunately I see no way to formally justify this.

3. Aug 28, 2009

### Staff: Mentor

Convert 1.13 deg C to Kelvin

273.15+1.13 = 274.28 or 274?

Not that I know what the answer to the original question is. Significant digits are faulty by design, and the deeper you look, the more messy it gets.

4. Aug 28, 2009

### symbolipoint

Converting to Kelvin seems like a good idea for achieving the best accuracy.

5. Aug 29, 2009

### Bohrok

What I learned tells me that the two decimal places in both numbers are significant, so the answer would be 274.28.

After thinking more about it, I'd say that 0 and 0.0 both have one significant digit even though I still can't think of a rule from the textbook that justifies it.