(This homework is only for First and Third Period Class. The one for Fourth Period is posted on Edmodo.)
We saw in class how to count significant figures. Here I will explain how to use the significant figures in Multiplication, Division, Adition and Substraction. Then you must go on Edmodo.com and solve the problems posted there.
Remember that there are three rules on determining how many significant figures are in a number:
- Non-zero digits are always significant.
- Any zeros between two significant digits are significant.
- A final zero or trailing zeros in the decimal portion ONLY are significant.
The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer.
This means you MUST know how to recognize significant figures in order to use this rule.
Example #1: 2.5 x 3.42.
The answer to this problem would be 8.6 (which was rounded from the calculator reading of 8.55). Why?
2.5 has two significant figures while 3.42 has three. Two significant figures is less precise than three, so the answer has two significant figures.
Example #2: How many significant figures will the answer to 3.10 x 4.520 have?
You may have said two. This is too few. A common error is for the student to look at a number like 3.10 and think it has two significant figures. The zero in the hundedth's place is not recognized as significant when, in fact, it is. 3.10 has three significant figures.
Three is the correct answer. 14.0 has three significant figures. Note that the zero in the tenth's place is considered significant. All trailing zeros in the decimal portion are considered significant.
Another common error is for the student to think that 14 and 14.0 are the same thing. THEY ARE NOT. 14.0 is ten times more precise than 14. The two numbers have the same value, but they convey different meanings about how trustworthy they are.
Four is also an incorrect answer given by some ChemTeam students. It is too many significant figures. One possible reason for this answer lies in the number 4.520. This number has four significant figures while 3.10 has three. Somehow, the student (YOU!) maybe got the idea that it is the GREATEST number of significant figures in the problem that dictates the answer. It is the LEAST.
Sometimes student will answer this with five. Most likely you responded with this answer because it says 14.012 on your calculator. This answer would have been correct in your math class because mathematics does not have the significant figure concept.
For addition and subtraction, look at the decimal portion (i.e., to the right of the decimal point) of the numbers ONLY. Here is what to do:
1) Count the number of significant figures in the decimal portion of each number in the problem. (The digits to the left of the decimal place are not used to determine the number of decimal places in the final answer.)
2) Add or subtract in the normal fashion.
3) Round the answer to the LEAST number of places in the decimal portion of any number in the problem.
WARNING: the rules for add/subtract are different from multiply/divide. A very common student error is to swap the two sets of rules. Another common error is to use just one rule for both types of operations.
Example 1:
98.123 + 6.6 = 104.723 but in order to follow the rule we have to round it up to 104.7 because 6.6 has only one decimal place
Example 2:
54.732 + 87.4321 + 9.3421 = 151.5062 but we have to round it to 151.506 because the number with the least decimal places has only 3 decimal numbers which is 54.732
Now go on EDMODO and do your work!
If you still need some help watch this video
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