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Chemistry 11 Name: _____________________
Ch 2.4 Blk: ______ Date: ____________
Ch 2.4 Significant Figures I
A) What is a significant figure (sig. fig.)?
A significant figure is a __________________ or meaningful digit.
Significant figure: is the _________________ number of digits needed to write a given value without ________________________.
Example 1:
At an Olympic trials race, a runner was claimed to have crossed the finish line at a time of 35.2168497 seconds. A stopwatch was used to time the runner during the race. What is wrong with the runners time?
If the stopwatch can only read to 0.1 s, then it is silly to claim that the time is
35.2168497 s. The stopwatch cant measure the time to 7 decimal places. Therefore, the last digits (168497) have no significance!
The time should be reported as ____________________________.
B) Accuracy & Precision
Precision describes the reproducibility of a result.
If you measure a quantity several times and the same number of significant digits agree closely with one another, your measurement is precise.
A precise measurement also has more sig. figs.
Accuracy describes how close a measured value is to the true value. If a known standard is available, accuracy is how close your value is to the known value.
Accurate & Precise Precise but not accurate
Example 2:
The accuracy and precision of your measurement is in your instrument. If you were to measure the mass of a tennis ball on two different types of scales they may have different measurements. Which balance is more accurate and precise?
Centigram balance: 54.4 g
Analytical balance : 54.4418 g
Rules of Significant Figures:
The number of significant figures in a measured value is equal to all the certain digits PLUS the first uncertain digit. Hence, zeros in the middle are also signifiant.
Eg. 35.2 ( First uncertain digit. (___ sig figs)
Certain digits.
E.g. 405 (___ sig figs)
Leading zeroes are NOT significant. Leading zeros are place holders.
Eg. 0.025 ( ___ sig figs)
Trailing zeroes are significant! Trailing zeros are located to the right of a decimal point.
Eg. 25.00 ( ___ sig figs)
25.0000 ( ___ sig figs)
Zeros preceding (before) the decimal point.
E.g. 70. ( __ sig figs)
Any zeroes at the end of a value are NOT significant when no decimal point is shown. (we assume that the last digits are zeroes because they are rounded off)
E.g. 10 ( ___ sig fig)
1100 ( ___ sig figs)
12500 ( ___ sig figs)
Practice Problems
1) Underline all significant digits in each question
a) 5 600 b) 8 060 c) 3.090 d) 0.0112
e) 0.002 f) 4.007 g) 0.0040 h) 0.0390
i) 0.00700 j) 8 000 k) 0.06 l) 120.0
2) Round the number 840.556 and write it with
a) five sig figs ________________________
b) four sig figs ________________________
c) two sig figs ________________________
one sig fig ________________________
Assignment: Hebden p. 28 #42, p. 29 # 44, 45, p.37 #55
Chemistry 11 Name: _____________________
Ch 2.5 Blk: ______ Date: ____________
Ch 2.5 Significant Figures II
A) Multiplying and Dividing Numbers:
After multiplying or dividing numbers, round off the answer to the LEAST number of significant figures contained in the calculation.
E.g.1) 2.00 x 3.000 00 =
E.g. 2) 3.26 x 10-5 x 1.78 =
E.g. 3) 48.6 / 8.91578 =
B) Adding and Subtracting Numbers:
After adding or subtracting numbers, round off the answer to the LEAST number of decimal places contained in the calculation.
E.g.1) Add 12.56 and 125.8 together.
. 12.5 6 ( 2 decimal places
+ 125.8 ( 1 decimal place
138.3 6
final answer rounded to 1 decimal place!
NOTE: You should keep all your digits used on your calculator during the
calculations. Only the final answer should be rounded!!!
You can only add the numbers when the exponents have the same power.
E.g.2) 18.9984032 E.g. 3) 1.234 x 106 + 4.568 x 107 = ?
18.9984032
_+ 83.80______
C) Mixed Calculations:
Multiply & divide before addition & subtraction.
Keep track of the number of sig. figs. at each step, but round off the # of sig. figs. at the end.
E.g. 1) 25.00 x 0.1000 15.87 x 0.1036
Practice Problems
1) Perform the following operations and express the answer with the correct number of sig figs.
a) 5.63 b) 873.6 c) 2.338
0.024 - 42.17 0.00041
+ 1.6470 + 55.00009
d) 263.12 e) 37800 = f) (160 + 2.7) =
x 120___ 18.00 (3.9)(678)
Exceptions to Sig. Fig. Rules:
Counting numbers and defined numbers are PERFECT numbers because they carry no uncertainty. Hence, they are exempt from sig. fig. rules.
.
Counting numbers
EXACT WHOLE numbers used in counting which involve things or living-things that cannot be subdivided. E.g. 24 students, 2 books
Defined numbers
Include conversion factors are used to define exact relationships.
E.g. 1 m = 100 cm, 12 =1 dozen (these are always true by definition!)
Example:
1) If it takes 12 hours by flight to travel from Vancouver to Dalian, how many seconds in the flight?
12 hours x 60 min x 60 s = ____________
1 h min
2) One molecule of sulphur contains 8 sulphur atoms. How many sulphur molecules can be made from 104 sulphur atoms?
104 atoms x 1 molecule = _________________
8 atoms
Assignment: Hebden p.39 #56#a-h, #57 f-j, #58 f-j and #59 all
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