What does it mean to use sig figs in your answer?

Question

Suppose this was the problem..

If a person weighs 165 lbs, how many grams does this person weight? The answer's 74,910 grams, but how do I write this properly, considering sig figs and all that? Rules and when to do what are appreciated.

Answer 1

Significant figures is a way in science to keep track of uncertainty in measurements. All instruments have a limit beyond which they cannot measure; for example, an analytical balance can measure items to 0.0001 grams. Something that weighs exactly 1.0234289345 grams would read 1.0234 grams on the balance. This number has 5 significan figures. The rules for using significant figures is as follows:
Any non-integer digit is significant
Any 0 between two non-zero digits is significant
Any leading 0 (before the integer, such as the 0's in 0.00123) is not significant.
Any 0 trailing a non-zero integer may or may not be significant.
a) it is significant if a decimal point is present (eg, 0.0340, the last 0 is significant)
b) it may or may not be significant if no decimal place is present

The above rules are general. That does NOT mean, however, if you punch two numbers (30 / 26) into your calculator, and you get an answer of 1.1538462, that all of those digits are significant. A measurement, such as 26 grams has 2 significant figures. A measurement of 30.0 mL has 3 significant figures. When you multiply or divide a series of numbers together, you can write the answer with the same number of significan figures as that of the number with the LEAST number of significant figures. Since 26 has 2, and 30.0 has three, you can write the answer of 30.0/26 to be 1.2, or with 2 significant figures. The rules are different with addition and subtraction. When you add or subtract two numbers, it is the decimal place, not the number of significant figures you look at. If you add 1.24, 1.56893, 11.1 and 1.452, you get 15.36093. You can write this, however as 15.4. You have to round your sum/difference to have the same number of decimal places, not the same number of significant figures, as the number with the LEAST number of decimal places. In the above series, that is 11.1, so you round to 1 decimal place. For your above question, you can write that as 7.49 X 10^4 grams, or 74.9 kg. The first method is scientific notation, so called because there is never any question about how many digits are significant when you use scientific notation.

Answer 2

Significant figures are fun: My rules for my class

All whole numbers are significant (1-9)/then the problem lies with that awful zero.
Any zero place between whole numbers are sig:
(1009) 4 SD Not hard to REM
Any zero that follow a whole number that follows a decimal is sig: 0.0010 2SD (the zeros before the decimal and in the tenths and hundredths place are just place holders. A measurement has not been determined until you get the the thousandths place and then the final zero is the guess for the final measurement that you could make with an instrument.
A zero at the end of a whole number is not sig:
10 (1 SD), 230 (2SD), 500 (2SD)
AND if you put a decimal at the end of a number like 10 (10.) then you have 2SD's. That means that the measurement was exactly 10, on the line.
10.0 would have 3 SD's. Because the number 10 is a whole number and your measuring instrument allowed you to measure to the tenths place. Our balance does this.

Answer 3

Basically, don't express answers that appear more precise than they really are. In your example, the person's weight is known to three significant figures (somewhere between 164.5 and 165.5). Just because you multiply that by 453.6 gm/lb doesn't increase precision, you still can be within a 28 gram "window" and have the same significant figures. Thus, you would report the answer as 74,900 or even bettter 7.49x10^4.

Rules are in most any physics or chemistry textbook. But basically, they boil down to, the least precise answer governs the number of significant figures.

Answer 4

Ok, i was just learning this in chemistry last week. I found the rules for you from a website.

Rule: All non-zero digits are significant.
12.83 cm [4] 16935 g [5]

Rule: Zeros between other significant figures are significant.
12 038 cm [5] 169.04 g [5] 70 304 g [ ] 395.01 kg [ ]

Rule: Zeros to the right of a decimal point and to the right of a number are significant.
12.380 cm [5] 169.00 m [5] 3.010 mL [4] 1.30 kg [ ] 1691.100 cm [ ]

Rule: A zero standing alone to the left of a decimal point is not significant.
0.421 g [3] 0.5 m [ ]

Rule: Zeros to the right of the decimal and to the left of a number are not significant.
0.000 421 mg [3] 0.001 80 cm [3] 0.010 kg [ ] 0.01010 m [ ]

Rule: Zeros to the right of the last number but left of the decimal point may or may not be significant. This information is known only to the person that made the measurement. Use scientific notation when in doubt. The use of a bar over the last significant zero is acceptable as well as using the decimal point to indicate that all digits to its left are significant.
4000. g [4] 3400 kg [2] 69 700. mL [ ] 4.50 E 2 g [ ]

I had trouble in class with this at first but i finally figured it out. I hope i helped you out!

Answer 5

exact amouint of digits
233.4 has 4 sig figs
23 has two
0.00005 has 1 [only hte 5 is sig nifficant