Transcript History of Measurement - Tredyffrin/Easttown School District

History of Measurement
VFMS 2014
Mrs. Long
Measurement Notes
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I. Historical units of measurement
Length
1. Cubit = distance from the tip of the elbow to
the tip of the middle finger.
2. Fathom = distance across a man’s
outstretched arms.
3. Span – distance from pinky to thumb on an
outstretched hand.
4. Digit – length of one finger.
Measurement Notes
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Weight
Babylonians improved upon the invention of
the balance by establishing the world’s first
weight standards – polished stones!
Egyptians & Greeks used a wheat seed as
the smallest unit of weight.
II. Timeline of measurement
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Thirteenth century – King Edward of
England, realized the importance of
standardization – ordered the “iron ulna”.
1793 – Napoleon’s rule of France, the metric
system was born! Based on the meter –
supposed to be one-ten–millionth
(1/10,000,000 ) of the Earth’s circumference
(measured at 40,000 km)
II. Timeline of measurement
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1960 – Officially adopted Systeme
International (SI System) need for universal
language in sciences recognized. Decimal
system is based on units of 10.
Today – Accepted & used worldwide by
scientist
III. Fundamental Units of Measurement
Quantity
Unit
Symbol
Length
meter
m
Mass
gram
g
Volume
liter
l
Time
second
s
Force
newton
N
Energy
joule
J
Metric System
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The metric system is based on a base unit that corresponds to
a certain kind of measurement
 Length = meter
 Volume = liter
 Weight (Mass) = gram
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Prefixes plus base units make up the metric
system
–
Example:
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Centi + meter = Centimeter
Kilo + liter = Kiloliter
IV. Using the Metric System
To convert to a smaller unit,
move the decimal point to the
right or multiply.
To convert to a larger unit,
move the decimal point
to the left or divide.
KING
HENRY
DECKED
BULLIES
DRINKING
CHOCOLAT
E
MILK
Kilo
Hecto
Deka
Base Unit
deci
centi
milli
H
D
Volume: liter (l)
Distance: Meter (m)
Mass: gram (g)
d
c
m
100.0
10.0
1.0
0.1
0.01
K
1000.0
Bigger
0.001
Smaller
Metric System
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Giga
G
The three prefixes that we
will use the most are:
– kilo
– centi
– milli
MEGA
M
KILO
k
LARGER than base unit
HECTO
h
DECA
D
Base
Units
meter
gram
liter
deci
d
centi
c
milli
m
smaller than base unit
micro

nano
n
Metric System
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These prefixes are based on powers of 10. What does this mean?
–
From each prefix every “step” is either:
 10 times larger
or
 10 times smaller
–
For example
 Centimeters are 10 times larger than millimeters
 1 centimeter = 10 millimeters
GIGA
G
MEGA
M
KILO
k
HECTO
h
DECA
da
Base
Units
meter
gram
liter
deci
d
centi
c
milli
m
micro

nano
n
Metric System
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If you move to the left in the diagram, move the
decimal to the left
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If you move to the right in the diagram, move the
decimal to the right
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Example #1
13.2 mg = ? g
Step 1: Identify that mg < g
Step 2: slide decimal point to the left 3 times
13.2 mg
Step 3: put a “0” in front of the decimal and add
correct unit to the number
0.0132 g
Example 2
5.7 km = ? cm
Step 1: Identify that km > cm
Step 2: slide decimal point to the right 5 times because
kilometers are 5 units larger than centimeters
5.7 km
Step 3: put four “0’s” in behind the 7 and add the correct
unit to the number
570,000 cm
Metric System
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Now let’s start from meters and convert to centimeters
500 centimeters
5 meters = _____
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
• Now let’s start from kilometers and convert to meters
.3 kilometers = _____
300 meters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Metric System
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Review
–
–
–
–
kilo
What are the base units for length, volume and mass in
the metric system?
What prefix means 1000? 1/10?, 1/1000?
How many millimeters are in 12.5 Hm?
How many Kiloliters are in 4.34cl?
hecto
deca
meter
liter
gram
deci
centi
milli
Metric System
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Now let’s start from meters and convert to kilometers
4
4000 meters = _____ kilometers
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
• Now let’s start from centimeters and convert to
meters
40
4000 centimeters = _____ meters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
V. Accuracy vs. Precision
1. Accuracy – nearness of a measurement to the
standard or true value.
2.
Precision – the degree to which several
measurements provide answers very close to each
other.
3. Percent error:
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a measure of the % difference between a
measured value and the accepted “correct” value
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formula:
| correct – measured | x 100 = %
error
correct
VI. Significant Figures- Certain vs.
Uncertain Digits:
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Certain – DIGITS THAT ARE DETERMINED USING
A MARK ON AN INSTRUMENT OR ARE GIVEN BY
AN ELECTRONIC INSTRUMENT
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Uncertain – THE DIGIT THAT IS ESTIMATED
WHEN USING AN INSTRUMENT WITH MARKS
(ALWAYS A ZERO OR FIVE – FOR THIS CLASS)
Significant figures
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Rules
Numbers other than zero are always significant
96 ( 2 )
61.4 ( 3 )
One or more zeros used after the decimal point is
considered significant.
4.7000 (
5)
32 (
2 )
Zeros between numbers other than zero are always
significant.
5.029 ( 4 )
450.089
( 6 )
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Zeros used at the end or beginning are not
significant. The zeros are place holders only.
75,000 ( 2 )
0.00651 ( 3 )
Rule for rounding-If the number to the right of the
last significant digit is 5 or more round up. If less
than 5, do not round up.
Need 2 sig figs. For this value 3420 (3400 )
Need 3 sig figs. For this value 0.07876 ( 0.0788)
Significant Figures
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Digits in a measured
number that include
all certain digits and a
final digit with some
uncertainty
Number
Number of Sig
Figs
9.12
0.192
0.000912
9.00
9.1200
90.0
900.
900
3
3
3
3
5
3
3
?
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Addition and Subtraction- answer may contain only as many decimals as the
least accurate value used to find the answer.
33.014+ 0.01 =
33.02
Multiplication and Division- answer may contain only as many sig. Figs. As the
smallest value used.
3.1670 x 4.0 = 12.668 13
Example State the number of significant
figures in the following set of measurements:
a. 30.0 g
b. 29.9801g
c. 0.03 kg
d. 31,000 mg
e. 3102. cg
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VII. Scientific Notation Scientific notation
Representation of a number in the form A x 10n
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Scientists work with very large and very small
numbers. In order to make numbers easier to
work with, scientists use scientific notation.
Scientific notation- there must always be only
one non-zero digit in front of the decimal.
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In scientific notation, the number is
separated into two parts. The first part is a
number between 1 and 9. The second is a
power of ten written in exponential form.
Examples: 100= 10x10= 102
1000= 10x10x10=103
0.1=1/10=10-1
.01=1/100=1/10x1/10=10-2
Converting numbers to Scientific
notation
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To write numbers in scientific notation, the
proper exponent can be found by counting how
many times the decimal point must be moved to
bring it to its final position so that there is only one
digit to the left of the decimal point (the number is
between 1 and 9).
A(+) positive exponent shows that the decimal
was moved to the left. It is moved to the right when
writing the number without an exponent.
A (-) negative exponent shows that the decimal
was moved to the right. It is moved to the left to get
the original number.
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Another method of deciding if the exponent is
positive or negative is to remember that values less
than one (decimals) will have negative exponents
and values of one or greater than one have positive
exponents.
Examples:
920=9.2x100=9.2x102
1,540,000=1.54x1,000,000=1.54x106
83500=8.35x10,000=8.35x104
0.018=1.8x.01=1.8x10-2
Scientific Notation
Representation of a number in the form A x 10n
Number
0.000319
3,190,000
0.000000597
Scientific Notation
3.19x10-4
3.19x106
5.97x10-7
Scientific Notation Computation Rules:
Addition and Subtraction:
1.make the exponents match
2.add or subtract the coefficients
3.keep the exponent the same for the answer
4.correct the S.N. if it is not in the correct format
2x103+3x103 =
1.5x103 + 2.6x104 =
Scientific Notation Computation
Rules:
Multiplication and Division:
1. multiply or divide the coefficients
2. add the exponents (for multiplication) or subtract the exponents (for
division)
3. correct the S.N. if it is not in correct format
1x102
X 1.2x105
1.7x103
X 2.3x10-1
7.3x10-4/ 4.2x102 =
Tools of Measurement
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Measuring Length
Ruler
Using the METRIC side
Record all certain digits PLUS one uncertain
(record to the hundredths place)
Units: cm, mm, m, km
Measuring Mass
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Triple beam balance
Uses three (sometimes 4) beams to measure the
mass of an object
Place solid object directly on pan
Place powders on filter paper or liquids in a
container; deduct mass of the paper or container
from the final measurement
Start with riders at largest mass and work back until
the pointer reaches zero
Record all certain (up to hundredths) plus one
uncertain (thousandths)
Measuring Volume
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Solids - Ruler
Volume = length x width x height
Units: cubic centimeter = cm3
Liquids – Graduated Cylinder
Read the volume at the bottom of the meniscus
Be sure to place the graduated cylinder on a flat surface and
look straight at the meniscus
Caution: Be sure to determine the increments on the graduated
cylinder
Record all certain (usually tenths) plus one uncertain (usually
hundredths)
Units: generally ml
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Unusually Shaped Objects – Water Displacement
Determine the volume of a filled graduated cylinder
Place the object in the graduated cylinder
Determine the volume of the graduated cylinder with
the object
Subtract the volume to determine the amount of
water displaced  the volume of the solid
Measuring Temperature
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Thermometer
Read the level of alcohol in the tube to
determine the temperature
Caution: When reading negative
temperatures be sure that you are reading in
the correct direction
Units: degrees Celsius
25 (F)
25 (C)
Temperature (C)
30 is hot
20 is nice
10 is chilly
0 is ice
The Metric System: Conversions
(APPROXIMATE)
Metric
1 kilogram
1 kilometer
1 meter
1 centimeter
1 liter
1 liter
English
2.2 pounds
0.62 miles
1.09 yards
0.39 inches
1.06 quarts
0.26 gallons