Transcript Introduction to Physics

Introduction to Physics
Science 10
Measurement and Precision
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Measurements are always approximate
There is always some error involved
Precision = the amount of information a
measurement involves
Deals with the smallest division on the
scale
Ex. Meter stick  readable to nearest mm
Estimating
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However you can estimate the readings
between the lines if you look carefully
Scientists agree to only add one additional
figure to their measurements in this way
Significant Figures
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Because the precision of all measuring
devices is limited, the number of digits for
measurement is also limited.
The valid digits are called significant
figures (or digits)
Ex. A ruler has 2 certain digits and we can
estimate 1 (9.40cm)
Digital Measurements
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The last digit is assumed to be estimated
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Ex. Digital balance reads 4.75g
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The 5 is estimated
Significant Figures
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It is a shorthand notation of showing error
in measurement in calculations and
experiments
When are digits significant?
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A Non-Zero is always significant
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EX. 22  2 sig fig’s
EX. 22.3  3 sig fig’s
With Zeros:
1)
Zeros placed before digits are NOT
significant
- Ex. 0.046L  2 sig fig’s
2) Zeros placed between digits are ALWAYS
significant
- Ex. 204  3 sig fig’s
With Zeros
3) Zeros placed after digits and after a
decimal are ALWAYS significant
Ex. 7.90  3 sig fig’s
4) Zeros at the end of a number are only
significant if there is a decimal after
Ex. 390  2 sig fig’s
390.  3 sig fig’s
How many sig figs?
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100000056
1.0256520
100
0.000006
0.01540250
3600.
3600
Rounding Numbers
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Often when doing arithmetic on a
calculator, the answer is displayed with
more significant figures than are really
justified.
How do you decide how many digits to
keep?
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Once you decide how many digits to
keep, the rules for rounding off numbers
are straightforward:
RULE 1. If the first digit you remove is 4
or less, drop it and all following digits.
2.6271 becomes 2.6 when rounded off to
two significant figures because the first
dropped digit (a 2) is 4 or less.
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RULE 2. If the first digit removed is
greater than 5, round up by adding 1 to
the last digit kept. 4.5832 is 4.6 when
rounded off to 2 significant figures since
the first dropped digit (an 8) is 5 or
greater.
RULE 3. If the first digit removed is
equal to 5 and the digit before it is an
even number, drop it and all following
Note about 5
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* If there are any numbers written after
the five, then you must round up.
Example: 1.245 is 1.24 when rounding to
3 sig figs
Example: 1.245000001 is 1.25 because
there is a number after the 5.
Adding And Subtracting
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When adding or subtracting, the number
of decimal places (not sig fig’s) in the
answer should be the same as the least
number of decimal places in either
number
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Ex.
5.67 J (2 DP)
1.1 J (1 DP)
+0.9378J (4 DP)
7.7 J
(1 DP)
Multiplying and Dividing
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Keep the least number of significant
figures in your answer that you have in
the numbers
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Ex.
1.2 m
x2 m
2.4 m
=2 m
(2 SF)
(1 SF)
(2 SF)
(can only keep 1 SF)