1. History of Measurement
VFMS 2014
Mrs. Long

2. Measurement Notes 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.

3. Measurement Notes 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.

4. II. Timeline of measurement
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)

5. II. Timeline of measurement
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

6. 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

7. Metric System Prefixes plus base units make up the metric system
The metric system is based on a base unit that corresponds to a certain kind of measurement
Length = meter
Volume = liter
Weight (Mass) = gram
Prefixes plus base units make up the metric system
Example:
Centi + meter = Centimeter
Kilo + liter = Kiloliter

8. IV. Using the Metric System
To convert to a larger unit, move the decimal point to the left or divide.
To convert to a smaller unit, move the decimal point to the right or multiply.
KING
HENRY
DECKED
BULLIES
DRINKING
CHOCOLATE
MILK
Kilo
Hecto
Deka
Base Unit
deci
centi
milli K H D
Volume: liter (l)
Distance: Meter (m)
Mass: gram (g) d c m
1000.0
100.0
10.0
1.0
0.1
0.01
0.001
Bigger
Smaller

9. Metric System The three prefixes that we will use the most are: kilo
centi
milli
Giga G
MEGA M
KILO k
HECTO h
DECA D
Base Units
meter
gram
liter
deci d
centi c
milli m
micro 
nano n
LARGER than base unit
smaller than base unit

10. Metric System
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

11. Metric System
If you move to the left in the diagram, move the decimal to the left
If you move to the right in the diagram, move the decimal to the right
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

12. 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 g

13. 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

14. Metric System Now let’s start from meters and convert to centimeters
5 meters = _____ centimeters
500
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Now let’s start from kilometers and convert to meters
.3 kilometers = _____ meters
300
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

15. Metric System
Review
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?
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

16. Metric System Now let’s start from meters and convert to kilometers
4000 meters = _____ kilometers 4
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Now let’s start from centimeters and convert to meters
4000 centimeters = _____ meters 40
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

17. V. Accuracy vs. Precision
1. Accuracy – nearness of a measurement to the standard or true value.
Precision – the degree to which several measurements provide answers very close to each other.
3. Percent error:
a measure of the % difference between a measured value and the accepted “correct” value
formula: | correct – measured | x 100 = % error correct

18. VI. Significant Figures- Certain vs. Uncertain Digits:
Certain – DIGITS THAT ARE DETERMINED USING A MARK ON AN INSTRUMENT OR ARE GIVEN BY AN ELECTRONIC INSTRUMENT
Uncertain – THE DIGIT THAT IS ESTIMATED WHEN USING AN INSTRUMENT WITH MARKS (ALWAYS A ZERO OR FIVE – FOR THIS CLASS)

19. Significant figures Rules
Numbers other than zero are always significant
96 ( ) ( )
One or more zeros used after the decimal point is considered significant.
( ) ( )
Zeros between numbers other than zero are always significant.
( ) ( )

20. Zeros used at the end or beginning are not significant
Zeros used at the end or beginning are not significant. The zeros are place holders only.
75, ( 2 ) ( )
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 (3400 )
Need 3 sig figs. For this value ( )

21. Significant Figures
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
9.00
9.1200
90.0
900.
900 3 5 ?

22. Addition and Subtraction- answer may contain only as many decimals as the least accurate value used to find the answer.
=  
Multiplication and Division- answer may contain only as many sig. Figs. As the smallest value used.
x 4.0 = 13

23. Example State the number of significant figures in the following set of measurements:
a g b g c kg d. 31,000 mg e cg

24. VII. Scientific Notation Scientific notation
Representation of a number in the form A x 10n
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.

25. In scientific notation, the number is separated into two parts
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: = 10x10= 102
1000= 10x10x10=103
0.1=1/10= =1/100=1/10x1/10=10-2

26. Converting numbers to Scientific notation
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.

27. 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=9.2x ,540,000=1.54x1,000,000=1.54x106
83500=8.35x10,000=8.35x =1.8x.01=1.8x10-2

28. Scientific Notation
Representation of a number in the form A x 10n

29. 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 =
1.5x x104 =

30. 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 1x x x10-4/ 4.2x102 = X 1.2x105 X 2.3x10-1

31. Tools of Measurement Measuring Length Ruler Using the METRIC side
Record all certain digits PLUS one uncertain (record to the hundredths place)
Units: cm, mm, m, km

32. Measuring Mass 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)

33. Measuring Volume 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

34. 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

35. Measuring Temperature
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

36. The Metric System: Conversions (APPROXIMATE)