physics Q3?

Question

How many digits should appear in a result expressed in the proper number of significant figures in 6.02 X 10^23 X 16.00 X 1.660 X 10 ^ -24 ?
Please explain how u worked out the problem

Answer 1

3 digits. Always follow the lowest number of significant figures of any component of the equation. which in this case is 6.02

Answer 2

I used to hate these questions. From my recollection (and a search of google), there are three rules to significant digits:

1) All nonzero digits are significant.
2) All zeroes between significant digits are significant.
3) All zeroes that lie to the right of the decimal point and the last nonzero digit from the right are significant.

When you add/subtract, you use the least accurate place. When you multiply/divide, you use the least amount of significant digits.

In the problem you posed:

6.02x10^23 has 3 significant digits (the 602 portion of the number)
16.00 has 4 significant digits (the 16 and the two 0's to the right)
1.600x10^-24 has 27 significant digits I believe (1 will be in the 24th position to the right of the decimal and the 660 will add 3 more).

So, your answer will have to have 3 significant digits. If I entered everything into the calculator right, the resulting answer would be 15.98912. Your resulting answer should only have three significant digits, thus you will use the "15" and one digit to the right of the decimal.

Rounding, your answer will be 16.0 I believe.

Answer 3

I still hate these questions! Here's what my gut says:
The number of signicant digits in any number should be the total number of digits between the 1st and last nonzero digits inclusive, plus the number of trailing zeros if you trust the source. (For an example of erroneous trailing zeros, look in any newspaper; you'll see stuff like "...the sun, at 93,000,000 miles distance...".)
OK, so 16.00 and 1.660 have 4 SDs. They are therefore accurate to ~1 part in 1600. And 6.02 is accurate to ~1 part in 600. Then the answer should be accurate to at least 1 part in 600 to avoid throwing away information. The number of SDs then depends on the value of the answer. If the 1st digit of the answer is 1, there should be 4 SDs; if 9, 3 SDs; if in between, use your judgment. When stretching beyond 1 part in 600, you can indicate uncertainty by putting the 4th digit in parentheses.
Using your question as an example, the answer is 15.9891.... I'd express it as 15.9(9), or if you are uncomfortable with parentheses, 15.99.
EDIT: All this leaves unanswered questions having to do with how the context of a number reflects on its accuracy. How do you decide that the number of significant digits in a number reflects its accuracy? E.g., "2" can a perfectly accurate number; nobody thinks that 2pi should be expressed as 6. But if I refer to a measurement as "2 miles", it may well not be exactly 2. What do you do if your teacher says to use 3.14 for pi, 6.02E23 for Avogadro's number or 9.81 for g? In homework do you treat those values as completely accurate? I think a lot of common sense and contextual insight must accompany such decisions. The ref. has some useful rules and observations on the subject including one which would clear up many ambiguities if always observed: Use scientific (x.y*10^n) or engineering (x.yEn) notation when the "trailing zeroes" rule is likely to be misunderstood, as in the above cited "93,000,000".

Answer 4

Three digits(?)