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Significant Figures
Slides saved as Sig
Fig Sci Notation 2
Finish up measurement lab
Go over homework/quizzes
Scientific Notation
Practice Problems
Homework tonight will be to complete the practice
problems. They are posted on the class website.
Navigate to our class section and download the word
document. If anyone would like a hard copy, let me
know.
Precision vs. Accuracy
Example: a 100-meter dash is timed by four different judges.
Here are the results:
Judge
Judge
Judge
Judge
1
2
3
4
9.58 s
9.6 s
11.5 s
10 s
Which is the most precise measurement?
Judge 1
Which is the least accurate?
Judge 3
Precision vs. Accuracy
Judge
Judge
Judge
Judge
1
2
3
4
9.58 s
9.6 s
11.5 s
10 s
Accuracy is how close the measurement is to the
actual value. Because Judge 3 had a time that
was significantly different than the others, we can
assume that her time was inaccurate.
Precision is a gauge of how exact a measurement
is. Therefore, the most precise measurement was
taken by Judge 1.
Significant Figures
What is the point of Significant
Figures (sig figs)
Different measuring tools offer different
precision
When using measurements in mathematical
calculations, you can only report the precision
of the least precise calculation that goes into the
measurement.
That is what sig figs is all about – reporting the
best answer possible and rounding off the
answer where appropriate.
…so which digits are considered significant?
1. All non-zero digits are significant
203.0, 0.404, 1000, 11.00
2. Zeros between significant figures are significant
203.0, 0.404, 1000, 11.00
3. All final zeros after the decimal point are significant 203.0,
0.404, 1000, 11.00
4. Zeros only used for spacing are not significant 203.0,
0.404, 1000, 11.00
If you see a number containing zeroes
with a decimal point at the end, that
decimal point means that these zeroes are
significant.
100. cm
7,700. mL
100,000,000. K
How many sig figs?
9200
0.0000212
0.002
1000
10.70
0.00600
900,010
1000.
Rounding rules for addition and
subtraction
If you add or subtract, the answer should be rounded to the same
number of decimal places as the measurement with the least
number of decimal places.
6.50 m
2 decimal places
5.3 m
1 decimal place
+3 m
0 decimal places
14.80 m
15 m is the answer you should report
Addition example
For example, let’s say you want to find the total mass of 3 fish.
Their masses are 12.1g, 11.23g, and 14.111g.
12.1 g
11.23 g
+ 14.111 g
37.441 g
Answer to report is 37.4 g
You cannot report your answer to the thousandths place because of
the fact that your least precise measurement only goes to the tenths
place!
sig fig rules for multiplication
and division
If you multiply or divide two numbers, the answer is
rounded off to the number of significant figures in the
measurement with the least number of sig figs.
12.011 g / 6.00 g = 2.0018333 g
5 sig figs
3 sig figs
The reported answer should be 2.00 g because it
has 3 sig figs
Division example
Lets say you wanted to determine the density of an object
that had a mass of 2.2 kg and a volume of 3.3 cm3
density = mass/volume
= 2.2 kg
3.3 cm3
= 0.6666666666666666666666666... kg/cm3
= 0.67 kg/cm3
Scientific Notation
Mass of the Earth
5,970,000,000,000,000,000,000,000 kg
Almost six septillion kilograms
Radius of a
carbon atom
0.00000000007 m
70 trillionths of a meter
Scientific Notation
• Used to write numbers that are very large or very small so that
they can be easily understood and used for calculations
• Conveys the number of significant digits and order of magnitude
Ever see “E” on a calculator?
E means “times ten to the”
5.124E12 =5.124 x 1012 m
Significant figures and scientific notation
The rules are the same for the number that
comes before the multiplier.
6.022 x 1023 atoms
4 sig figs
You can use scientific notation to report your
answer in the appropriate number of sig figs
• 1500 cm x 15 cm = 22,500 cm2
2 sig figs
2 sig figs
your reported answer can only have two sig figs,
therefore it could be 23,000 cm2 or 2.3 x 104 cm2
Sometimes you need scientific notation to express
the correct number of significant figures
Calculate the area of a factory with a length of
340 m and a width of 29.5 m.
(340m)(29.5m) = 10300m.
You need 2 significant figures. How can you write
10300m with 2 sig figs?
1.0 x 104 m
Significant figures in scientific
notation
• An electron's mass is about
0.00000000000000000000000000000091093822 kg.
• In scientific notation, this is written 9.1093822×10−31 kg.
• Note that all the zeros before the 9 are not significant.
Adding and subtracting with
Scientific Notation
You can only add and subtract in scientific notation if
the exponents are the same
If the exponents are the same, you just add or
subtract the numbers and leave the exponent alone
Here is an example: 4000 + 2000= 6000
In scientific notation 4000 = 4 x 103
and 2000 = 2 x 103
(4 x 103 ) + (2 x 103 ) = 6 x 103
Note that the numbers were added, but the
exponents remained the same
Adding and subtracting with
Scientific Notation
If you have two numbers in scientific notation, you
have to make the exponents the same before you
can add or subtract
Here is an example:
10,000 – 5,000 = 5,000
(1 x 104) – (5 x 103)
You need to change one of them so that their
exponents are equal!
(10 x 103) – (5 x 103) = 5 x 103
Multiplying with scientific notation
• When you multiply in scientific notation, you multiply the
numbers and then add the exponents.
• (3.2 x 107 )(1.0 x 1010) = 3.2 x 1017
• (2.5 x 1012)(2.00 x 10-4) =
5.0 x 108
Dividing with Scientific
Notation
When you divide in scientific notation, you divide the
numbers and then subtract the exponents. Here is an
example:
6.2 x 1012 = 2.0 x 107
3.1 x 105
9.0 x 10-16 = ???
3.00 x 105
= 3.0 x 10-21
Practice Problems!
1.
find the total mass of 20.2 kg and 11.00 kg
2.
find the area of a rectangle that has a length of 10.0 m and a
width of 12.34 m (a=l x w)
3.
find the change in mass of a 2.00 kg piece of dry ice that lost 0.50
kg
4.
find the change in mass of a 4.00 kg piece of dry ice that lost 0.5
kg
5.
find the density of a sample of water that has a mass of 0.0050 g
and a volume of 0.005 cm3 (d=m/v)
6.
find the total volume of 2 objects that are 2.33 x 103 L and 1.0 x
102 L
More Practice!
7.
multiply 3.05 x 1010 km and
2.1100 x 105 km
8.
divide 6.00 x 1015 m by 3.0 x 105 m
9.
40.20 sec/20.1000 m
10.
(6.6 x 10-6) (3.30 x 10-2)
11. 3000 + 200
12. 4000/200
More practice! Put the following numbers in scientific
notation with the appropriate number of sig figs!
13. 103,000
14. 105,000.0
15. 0.00004
16. 0.000000890
17. 0.0000001204
18. 198,000,000,000
19. 30
20. 0.5000