Significant Digits: Questions & Answers

[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?

 

[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 into 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.

 

[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')

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?

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

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

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

 

[xCanx]

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.

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.