# Significant digits

1. Jun 4, 2006

### Jessehk

I apologize in advance if this topic does not belong in the section of the forum -- it was the closest match I could find.

I am a grade 10 high school student (16 years old), and I was having a bit of a discussion with my science teacher (who was previously a chemical engineer).

I respect his knowledge, and I am sure that he knows exactly what he is talking about (I am not in the habit of questioning teachers), but he is a new teacher, and perhaps he is not doing things the standard ways.

We were looking at significant digits for use in simple Physics equations,
such as $$a = \frac{\Delta v}{ \Delta t}$$ .

In our textbook, it states that numbers such as 1000 have 1 sig fig, while he says that it has 5, and to represent 1000 as 1 sig fig, one could write $$1_{000}$$.

I looked around a bit, and found that the amount of sig figs in numbers with trailing 0's is debatable. I was wondering what the popular opinion of the members here is regarding this matter.

Thanks :)

Last edited: Jun 4, 2006
2. Jun 4, 2006

### rcgldr

I would regard 1000 as 4 significant figures. 1000.0 would be 5. Trailing zeroes count, since they distinguish between 1000 and 1001. Rewritten as 1E3 or 1 x 10^3, it would be one significant digit.

3. Jun 4, 2006

### Meir Achuz

It is a matter of context, as you say. Most people, even scientists are not careful to use special notation for 1000. Some instances:
1. If I owe you \$1,000, that is 4 sf.

2. If 1,000 people attended the rally, that is probably 2 sf. (more than 900, but less than 1100.
I often say the proton mass is 1,000 Mev, even though it is really 938.3 (to 4 sf). That 1,000 is about 1 or 2 sf.

3. Saying 1,000.0 is 5 sf (although some would call it 4 sf because a leading one is sometimes not considered an sf.

4. For your case, if a car travels 1,000 miles in 16:24 hours, I would still give the mph to 2 sf, but I am not a high school teacher. They have to follow stricter rules.

Last edited: Jun 5, 2006
4. Jun 4, 2006

### Jessehk

I didn't realize the topic was so subjective.

Thanks to both of you. :)