# Homework Help: Significant Digits

1. Sep 6, 2007

### xCanx

I just started physics and have a few questions on significant digits.

I have to put this number into scientific notation

2 999 900

My answer is 2.3 * 10 (to the power of 6)
Is that right?

My other question is 8.83/0.002 = "4415"
To write it with sig digits I can only use one because of "0.002"

So would my answer be 4000?

And my last question is 8.56 * 2.3= "19.688"
With sig. digits = 20

Are these correct?

2. Sep 6, 2007

### drpizza

In the first case, your answer is not quite correct with 2 significant digits. The number you had though, has at least 5 significant digits. The zeros are generally not counted unless there is a trailing decimal placed. Note that 2.9999 doesn't round off to 2.3

Also, on your last problem, it would be better to put a decimal in to show that the 0 is significant.

The last significant digit shows where any uncertainty lies - i.e. 245.8 might actually be 245.9 or maybe 245.7. If you measured a quantity, and were fairly certain to within 100 feet and had a measurement of 3,000,000 feet, how could you show where the uncertainty lies? That's another good purpose of scientific notation. You could write the number as 3.0000 x 10^8 feet.

Easiest rules on sci notation:
Any digits that aren't a zero always count.
zeros in front don't count.
zeros between other non-zero digits always count.
zeros at the end only count if there's a decimal.

3. Sep 6, 2007

### qspeechc

You need to state to how many significant digits you are using. Say, "to 2 significant digits".

If it were the case that you need two significant digits, then 2 999 900 in scientific notation would become 3.0*10^6 (the ^ means 'to the power')

I don't understand what you are trying to say.

Again you have to state to how many significant figures you are working with.

4. Sep 6, 2007

### xCanx

It's just multiplying and dividing (in physics) with significant digits.

In the second one

8.83/0.002 = "4415"

4415 isn't the answer because it has to have only 1 significant digit because 0.002 has only one significant digit. So I put 4000 as my answer because it only has one significant digit.