W H E R E M A T H B E C O M E S R E A L I T Y !

Measurement standards
 Quantities such as:
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Time
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Distance or length
“weight”
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Light brightness
MANY standards of measure have been used over the years.

Do you recognize any of these units?
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Millennium
Slug
Bushel
Kilogram
Calorie
Cubit
Foot-pound
Fahrenheit

Only 7 quantities can be measured directly!
Quantity
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Time
Mass
Distance or length
Temperature
Amount of substance
Amount of electricity
Light brightness
Base Unit
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Second
Kilogram
Meter
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Kelvin
Mole
Ampere
 Candela

...everything else is calculated!
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Speed
Current
Energy
Volume
Weight
Force
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…Which we call “derived” units…
 What do you think “modified” units might be?

“metric” system
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Actually, called “SI” for systeme international a worldwide agreement among scientists to adopt this method of measurement.
Also called, “kg-m-s” system for
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Kilogram
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Meter
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Second
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Should US officially adopt?

Refresher……

Accuracy vs. Precision
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Accuracy – how close a measured value is to an accepted value
Precision – how close a series of measurements compare to one another
Sucrose density – 1.59 g/mL
Trial 1
Trial 2
Trial 3
Average
Student A Student B Student C
1.54 g/mL
1.60 g/mL
1.40 g/mL
1.68 g/mL
1.70 g/mL
1.69 g/mL
1.57 g/mL
1.57 g/mL
1.45 g/mL
1.51 g/mL
1.71 g/mL
1.70 g/mL

Precision
 Measurements are as only as specific as the instrument being used.
 Consider a ruler marked in whole inches OR a ruler marked in tenths of inches.
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This is called the “precision” of the instrument and is indicated by the number of places used in writing the measurement.

For example….
 That ruler marked in whole inches can only be written down to the tenths place.
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10.5
1.7
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8.3
 Matter of fact, since the “tenth” was estimated, anyway, it is called a “guess digit”.

How about the ruler marked in tenths?
 Well, you could estimate in the hundredths place.
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10.58
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1.46
0.58
 Consider the measurement 11.20 inches using that ruler……why write the “zero”?

Scientific Notation Refresher….
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The Arabic number system is based on 10!
10 1 is one decimal place, right?
What about 10 -3 ?

Scientific Notation
 Two factors:
1.
A number between 1 and 10
2.
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
10 raised to a power (exponent)
Tells how many times the first factor must be multiplied by
10
Positive exponent – larger than 1 (move decimal to right)
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
Negative exponent – smaller than 1 (move decimal to left)
Examples:
1392000 – 1.392 x 10 6
0.000000028 – 2.8 x 10 -8

Which numbers are significant?
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All non-zeroes.
72.3
Zeroes between non-zeroes.
60.5
All zeroes to the right of a non-zero if the number contains a decimal.
6.20, 620
NEVER leading zeroes!
0.0253, .00054
Counting numbers and constants do not count as sig figs.

Significant Figures
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When adding and subtracting: Answer must have the same # of digits to the right of the decimal point as the value with the fewest digits to the right of the decimal point
Example: 28.0
23.538
+25.68
77.218 = 77.2

Significant Figures
 Multiplication and Division: Answer must have the same # of significant figures as the measurement with the fewest sig figs.
 Example: Volume of an object with dimensions
L = 3.65 cm, W= 3.20 cm, H= 2.05 cm
3.65 x 3.20 x 2.05= 23.944 cm 3
How m any sig figs does it need?

Whew! Let’s summarize…
 Measured quantities are used to calculate other quantities of interest.
 Those measurements come in a variety of scales and definitions, SO we all have to agree on a system.

Measurements are written in such a way as to indicate the precision of the instrument used.

Next….
 How does that precision get indicated when we calculate with the number?
 In other words, if I’m calculating with two numbers: one is made to the tenths….another is measured to the thousandths, where should I round my answer?
How precise can my calculation be?