How many significant figures in 500?

Question

Is it 1 or 3. I have had different chemistry teachers tell me different answers. Please explain why, or direct me to some authoratative source.

Answer 1

You cannot tell for sure, and the different teachers should have said that, and not given you a definite answer. Scientific notation is used to avoid ambiguities like this.

You might have weighed out exactly 500 grams of sodium chloride with a precision of +/- 0.5 grams. So the actual weight could have been anywhere between 499.5 grams and 500.5 grams, and the balance rounded to 500.

In this case, you weighed something to 3 significant figures, that in scientific notation would be 5.00 x 10^2.


Or you might have weighed 500 pounds of mulch, and your scale only showed a number every hundred pounds, and you could tell the pointer was closer to 500 than 600 or 400. So the actual weight of the mulch could range from 450 pounds to 550 pounds, that you rounded to 500 pounds.

In this case, you have one significant figure, that in scientific notation would be 5 x 10^2.


Now if you had weighed something to the nearest tenth of a kilogram, you could have reported 500.0 and there is no question that you weighed to four significant figures. The actual weight could have been between 499.95 up to 500.05 kilograms.


Now if you have some context to your number, sometimes you can be more definite. On an income tax return, you can round to the nearest dollar. So when you report $500 on some line of your 1040, the IRS interprets the number as really $500, not $501 or $499.

In the world of finance, generally all figures reported are significant. Like the budget of the United States. When a budget line item for DoD is 1,000,000,000 (one billion), it is really one billion, and not a dollar more or less.

One final caveat. Because of typographical errors and the liklihood a period "." might be overlooked, careful scientists NEVER write a number like 1/10 as .1, they always use 0.1, to emphasize that there is a decimal point.

Answer 2

Well,
Your in luck, I am a chemist. There is only 1 significant figure. The reason being is because if someone came up to you with a result and they said its 500, how do you know if it was 501 and they rounded, which would make it 500. 501 has 3 significant figures because the 0 is in between two non-zero numbers. If the number was 500.0, then there would be 4 significant figures, the zero after the dot signifies that the 500 is actually an exact number. Because there is no decimal to signify that 500 is an exact number, it has only one significant figure. Print this out if you want to and show your teachers, this is correct, and I know it is correct from experience and learning, this is guarantied right. Hope this helps.

Wee Man.

Answer 3

If it was something weighed to the nearest unit place it would be written 500. That is 500 with a decimal point. Without the decimal point, it as 1 significant figure. 500. has 3 sidnificant figures. With 500 you cant tell if it was 490 or 504. Either could be rounded to 500.

Answer 4

Trust me it is 1. A reason why is that the 2 zeros are accounted for when there is a decimal, before and after ".500" or "500.". Thus, vice versa.
.500---3 sig fig
.0500---3 sig fig
Look in your book!!

Answer 5

Second dude is right- you only count zeros as significant if they are to the right of the decimal point.

Answer 6

3..........
Because all numbers after a non zero digit is considered to be a significant number

Answer 7

1 you dont count the 0 at the end
u count the 0 s if only after the decimal
0.0362---------4
0.3620---------4
560--------------2