Transcript Measurement

MEASUREMENT
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Numbers are very important in science and the
way in which scientists interpret them must be
uniform. In other words, all scientists must be
speaking the same language so they can
understand one another.
In science a procedure called peer review is
utilized. In this process an individual does an
experiment and wants to give the information to
the science community. She/he publishes it in a
scientific journal so other scientists can look at
their work. Some scientists then try to repeat
the experiment and see if they can produce the
same results. This insures that people have not
made mistakes or lied about their research.
DATA
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Therefore when numbers are used as data
(quantitative data) we must understand what
we mean by them.
The numbers we use are from experiments in
which we measure things.
Some things can be measured exactly while
others cannot.
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People can be measured exactly because it is done one
by one. However, other things like the length of a
piece of paper cannot be measured exactly.
Your measurement depends on how precise your
instrument is.
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One of the rulers above (when measuring in inches) is
more precise. Which one and why?
Why is this important?
SIG FIG RULES
There are a few rules we will learn to determine the
number of significant figures in a number:
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Numbers for data that are counted one by one have INFINITE
significant figures.
All numbers 1-9 are significant
Zero’s are significant EXCEPT when:
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Trailing zeros: The number is greater than 1, there is no
decimal and they are at the end of a number.
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EX:
3,000 (The last 3 zero’s are NOT significant)
EX: 3,000. (These zeros ARE significant)
Leading Zeros: The number is less than 1 and they appear at
the front of a number.
• EX:
0.0002 (The first 4 zeros are NOT significant)
• EX:
0.000200 (The first 4 zeros are NOT significant but the
last
two ARE.)
Middle zeros: Zeros in between to significant digits are always
significant.
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EX: 2020 (the middle zero is significant but the last one is
not)
EX: 0.000040010 (the leading zeros are not significant but the
middle and trailing zeros are)
PRACTICE TIME
State the number of significant numbers in each set:
1. 0.020003 = ____
2. 0.0002300 = ____ 3. 0.000103 = ____
4. 0.0009
5. 0.0000033 = ____ 6. 0.000900 = ____
= ____
7. 2,000,000= ____
8. 500.
= ____ 9. 500.000 = ____
10. 8020
= ____
11. 90,000
= ____ 12. 208,030 = ____
13. 8,000.
= ____
14. 80,200
= ____ 15. 23.00
= ____
= ____
16. 3340.0 = ____
17. 90
18. 0.000
19. 2000
= ____
20. 200,000 = ____ 21. 2000.
22. .8070
= ____
23. 0.02020 = ____ 24. 0.03003 = ____
= ____
= ____
SCIENTIFIC NOTATION
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Instead of using standard notation scientists write numbers in
scientific notation. This system uses the base 10 as a multiplying
factor to move the decimal place around.
X 100 = times 1
X 101 = times 10
X 10-1 = times .1
X 102 = times 100
X 10-2 = times .01
And so on……. The base 10 moves the decimal around. So
why do we use this? The answer is simple. In science we
commonly have to use numbers that are very large or very small
and scientific notation is easier to use than standard notation.
For example the number of atoms in 12.01 grams (1mole) of
carbon is:
602,000,000,000,000,000,000,000
This would be a pain to write so instead we use: 6.02 X 1023
SCI. NOT. RULES
So how do we do this? Here are some general rules:
 The decimal place should be moved to the right of
the first non-zero number.
 The number in front of the base 10 needs to be a
number 1 – 10.
 The number of times you move the decimal
becomes the superscript of the base 10. Positive if
the number is greater than zero and negative if
less than zero.
 NOTE: Only significant numbers are included in
scientific notation.
CONVERT THE STANDARD NOTATION INTO
SCIENTIFIC
(WATCH YOUR SIG FIGS)
1. 660,000 = ___________2. 8,000. =
____________
3. 9050 = ___________4. 5,001 =
____________
5. 2.000 = ____________6. 4403.0 =
____________
7. 0.0120 = ___________8. 0.0500 =
____________
9. .00202 = ____________10. 0.0020 =
____________
STANDARD
(WATCH YOUR SIG FIGS)
6.02 X 10-4 = ____________________
2. 2.02 X 10-8 = ____________________
3. 2.00 X 10-5 = ____________________
4. 9. X 10-2 = ______________________
5. 9 X 100 = _______________________
6. 5.0089 X 106 = ___________________
7. 3.0 X 105 = _____________________
8. 3 X 106 = _______________________
9. 5.000 X 101 = ___________________
10. 4.00 X 102 = _____________________
1.
ROUNDING
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What is rounding?
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It comes from the
idea that some
numbers are
irrelevant or not
significant and
therefore not
reliable.
In science, we do
not round like
math. We must
round to the
appropriate number
of sig figs.
1) 15.6
 2) 15.6
 3) 690
 4) 5,555
 5) 8.12 X 104
 6) 9.5 X 102
 7) 4.5 X 104
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(1)
(2)
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ROUND THE VALUE TO THE NUMBER OF SIG. FIGS.
INDICATED BY THE PARENTHESIS.
1.
555.5 (1)______ 2. 7.586500 (4)______ 3. 650 (1)_______
4. 0.0055 (2)______ 5. 1.500 (1)________ 6. 0.3400 (1)______
7.
428.09 (3)______ 8. 666,500. (4)______ 9. 0.7500 (1)_____
10. 0.0630 (1)______ 11. 0.4355 (1)________12. 9.50 (1)_____
13.
995. (2)________ 14. 199,500 (3)______
15. 2.9995 (4)_______
SIG FIG CALCULATIONS
 As
has been discussed, numbers are very
important and their reliability is crucial
when using them for practical applications.
 When doing science we often take the data
that we have measured and manipulate it to
find a multitude of other information.
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In other words, we take the numbers from our
experiment and we will add, multiply, subtract,
and divide them in order to calculate other derived
quantities.
 However,
the problem arises in that all
numbers are NOT created equally.
ADDITION & SUBTRACTION
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Look at all the numbers that are in your
calculation and determine which has the least
number of decimal places. Your answer should
have the same number of decimal places as this
one. (Units must be the same)
EX: 1.230g +12.5g + 25.36521g = 39.0 9521
Final answer rounded = 39.1g
MULTIPLICATION & DIVISION
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Look at all the numbers that are in your calculation
and determine which has the least amount of
significant figures. Your answer should have the
same number of significant figures as this one.

Treat units like variables in algebra
3,000. m3 = 300 m = 3.0 X 102 m
10. m2
 EX:(12.220 ft) X (11ft) = 13 4.42 ft2 = 130 ft2

EX:
CALCULATION PRACTICE
1. 654.0g5/6g = ___________________2. (5500m-9)(56.m) = _________________
3. 8.632 nm+ 8.3 nm – 30.0 nm = _____
4. 18 g +6.80 L+0.050 L– 226 =_____
5. (60.0g)/(230 cm3) - .0520g/cm3 = ______6. (0.020ml)(300.560ml) + 1 ml2 =___
7. 6.9 X 107 nm3 / 4.00 X 107 nm = _______ 8. (1 X 107 kg3)(2.45 X 10-4 ft-3) = ___
9. 2.55 X 102 ml4 + 6.6 X 103 ml4 = _______10. 4 X 10-2 ft2 - 2.00 X 10-3 ft-3 = ____
11. (6.9 X 107 Kg3 / 4.00 X 106 Kg3) - 8 X 101 kg- 2.3 X 101 kg3________________