Transcript tv 82 cm

Significant Digits
Scientific Notation
Dimensional Analysis
 Counting numbers have an infinite number of
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significant digits because they’re derived from…
counting. (You can’t have two and a half cars.)
Measured numbers are precise to a point and the last
digit is an estimate.
How tall are you?
79” vs. 79.25”
2 m = 201 cm
201 cm or 201.3 cm
 Going to the moon.
 Have Direct TV
 Going to mars?
Number
# of Sig Figs
 25
 2
 0.25
 2
 301
 3
 3.01
 3
 40
 1
 400
 1
 40.00
 4
 0.040
 2
Number
# of Sig Figs
 25
 2
 0.25
 2
 301
 3
 3.01
 3
 40
 1
 400
 1
 40.00
 4
 0.040
 2
All nonzero numbers are always significant. (25)
2) Any zero between two significant digits is also
significant. (301)
3) Leading zeroes are never significant. (0.01)
4) Final zeroes (ending zeroes) are only significant if
they follow (to the right of) the decimal. (300, 3.0,
3.00)
 337.2
 1004
 0.00300
1)
Multiplication and Division are not the same as those for
Addition and Subtraction.
 Your answer can be no larger than the number with the
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fewest significant digits.
27.2 x 3 =
81.6 or 82 or 80? (3 s.d. or 2 s.d. or 1 s.d.)
8.92/3.2 =
2.7875
2.8
 Answer can be no more precise than the least precise
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number.
6.26 + 3.1 = ?
9.36?
9.4
27 + 1.9752 =
29
 Useful when numbers are very large or very small
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(678,000,000,000,000,000,000,000,000)
Also useful to express a number in significant digits.
(5,000 to two sig figs.)
All numbers can only be expressed as the product of a
number between 1 & 9 inclusively and a whole-number
power of ten.
So 5,000 would be 5.0 x 103.
678,000,000,000,000,000,000,000,000 =
6.78 x 1026
2
3
x
3 =
4
2
3
x
3
4
6 = 1
12
2
2
3
x
3 =
4
1
3
x
3
2
6 = 1
12
2
2
3
x
3 =
4
1
3
x
3
2
6 = 1
12
2
2
3
1
1
x
3 =
4
6 = 1
12
2
x
1
2
1
2
=
 This concept also works with units.
 Since there are twelve inches in one foot then…
6.5 feet = ? inches
 This concept also works with units.
 Since there are twelve inches in one foot then…
6.5 feet x 12 inches = 78 inches
1 foot
Conversion factor
 How far is it to the sun?
 Need to know the speed of light is 186,000
miles/second
 Light takes 8 mins to get to earth from the sun.
 Work it out!
8 mins x 60 s x 186,000 mi =
min
s
 How far is it to the sun?
 Need to know the speed of light is 186,000
miles/second
 Light takes 8 mins to get to earth from the sun.
 Work it out!
8 mins x 60 s x 186,000 mi = 90,000,000 mi
min
s
 9 x 107 mi