1. History of Measurement
VFMS 2013
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. 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

8. 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

9. 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)

10. 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.
( ) ( )

11. 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 ( )

12. 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 ?

13. 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

14. 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.

15. 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

16. 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.

17. 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

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

19. 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

20. 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)

21. 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

22. 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

23. 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

24. The Metric System: Conversions (APPROXIMATE)