1. Metric Measurement, Scientific Notation, & Sig Figs
Unit 1 Section 2
Metric Measurement, Scientific Notation, & Sig Figs

2. The International System of Units
If everyone is to understand what your measurements mean, you must agree on the units that will be used.
By international agreement, a set of units called "The International System of Units" has been defined for scientific work. This system was adopted in 1960 by the General Conference on Weights and Measures.
These units are also called metric units or SI units.

3. SI has seven base units meter m kilogram kg second s or sec Kelvin K
Quantity
Unit Name
Unit Abbreviation
Length
meter m
Mass
kilogram kg
Time
second
s or sec
Temperature
Kelvin K
Amount of Substance
mole
mol
Electric Current
ampere A
Luminous Intensity
candela cd

4. It is universally understood.
Advantages of Using SI
SI Units make measuring and calculating easier. Measurements are always expressed as decimals rather than fractions.
It is very easy to change from one unit to another since they are based on 10.
It is universally understood.

5. SI Prefixes
Prefixes can be placed in front of the base units. These prefixes are used to represent quantities that are larger or smaller than the base units. These prefixes must be memorized.

6. Prefix Meaning Unit Abbreviation Giga- G 1,000,000,000 (billion) Mega-
1,000,000 (million)
Kilo- k
1,000 (thousand)
Hecto- h
100 (hundred)
Deca- da
10 (ten)
(Base)
UNITS with NO PREFIX 1
Deci- d
.1 (tenth)
Centi- c
.01 (hundredth)
Milli- m
.001 (thousandth)
Micro- 
(millionth)
Nano- n
(billionth)

7. Conversion of Metric Units
To convert from one metric unit to another, count how many “steps” it takes to get to the desired level. If you go UP, move the decimal to the RIGHT. If you go DOWN, move the decimal to the LEFT.

8. Metric Conversion Examples:
86,000
1) 86 g = _______________ mg
98.24
2) 9824 cL = __________________ L
.872
3) 872 µs = _______________ ms
4) .678 g = _______________ kg
1,000,000
5) 1 km = _______________ mm

9. Metric Unit of Length .000001 m .001 m .01 m .1 m 10 m 1000 m
The meter (m) is the SI base unit of length.
Prefixes are used to indicate distances longer and shorter than a meter.
Length: straight line distance between 2 points.
What name and symbol is given to each of the following
units of length? m
.001 m
.01 m
.1 m
10 m
1000 m
Micrometer m
Millimeter mm
Centimeter cm
Decimeter dm
Decameter dam
Kilometer km

10. The cubic meter (m3) is the SI derived unit for measuring volume.
Metric Unit of Volume
Volume:
How much space something takes up.
The cubic meter (m3) is the SI derived unit for measuring volume.
When chemists measure the volumes of liquids and gases, they often use a non-SI unit called the liter.
mL and cm3
The two units, _________________, are interchangeable.

11. The ____________is the SI base unit for measuring mass.
Metric Unit of Mass
Mass:
The amount of matter in an object.
Weight:
Force with which gravity pulls on matter.
Mass and weight are often confused. Mass is not affected by gravitational pull.
Your weight on the moon would be less, but your mass on the moon would be the same.
The ____________is the SI base unit for measuring mass.
kilogram (kg)

12. State the quantity that is measured by each of the following units:
Mass
Length
Temperature
Time
1. centigram
2. millimeter
3. Kelvin  
4. millisecond

13. Scientific Notation
Why? So scientists can easily express numbers that are very large and/or very small.
Examples:
The mass of one gold atom is
grams.
One gram of hydrogen contains
hydrogen atoms.
Scientists can work with very large and very small numbers more easily if the numbers are written in scientific notation.

14. What is Scientific notation?
In scientific notation, a number is written as the product of two numbers…..
….. A simple number (coefficient) multiplied by a power of 10

15. 1. Move the decimal to the right of the first non-zero number.
HOW to write a number in scientific notation:
1. Move the decimal to the right of the first non-zero number.
2. Count how many places the decimal had to be moved.
3. If the decimal had to be moved to the right, the exponent is negative.
4. If the decimal had to be moved to the left, the exponent is positive.
** Scientific Notation can be reversed to write the number in standard form again.

16. For example: The coefficient is _________.
The number 4,500 is written in scientific notation as ______________.
The coefficient is _________.
4.5
The coefficient must be a number greater than or equal to 1 and smaller than 10.
The power of 10 or exponent in this example is ______. 3
The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500.

17. Practice Problems PROBLEMS ANSWERS .00012 1.2 x 10-4 1000 1 x 103 0.01
Put these numbers in scientific notation.
PROBLEMS
1.2 x 10-4
1 x 103
1 x 10-2
1.2 x 101
9.87 x 10-1
5.96 x 102
7.0 x 10-7
ANSWERS
.00012
1000
0.01 12
.987
596

18. EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS
PROBLEMS
ANSWERS
4.9 X 102
3.75 X 10-2
5.95 X 10-4
9.46 X 103
3.87 X 101
7.10 X 100
8.2 X 10-5
490
.0375
9460
38.7
7.10

19. What are significant Figures (aka Sig Figs)?
The significant digits in a measurement are all of the digits known with certainty plus one final digit, which is uncertain or is estimated.

20. For example: Study the diagram below.
Using the ruler at the top of the diagram, what is the length of the darker rectangle found in between the two rulers?
Answer: The length is between 4 and 5 cm. The “4” is certain, but the distance past 4 cm will have to be estimated. A possible estimate might be Both of these digits are significant. The first digit is certain and th second digit is uncertain because it is an estimate.

21. Using the ruler at the bottom of the diagram, what is the length of the darker rectangle found in between the two rulers?
Answer: The edge of the rectangle is between 4.2 cm and 4.3 cm. We are certain about the 4.2, but the next digit will have to be estimated. As possible estimation might be All three digits would be significant. The first two digits are certain and the last digit is uncertain.

22. Please remember…
The last digit in a measurement is always the uncertain digit.
It is significant even if it is not certain.
The more significant digits a value has, the more accurate the measurement will be.

23. There are a few rules that determine how many significant digits a measurement has. You will need to Learn these rules!

24. Rule #1: Non-zero digits are ALWAYS significant.
Rule #2: Any zeros between sig figs ARE significant.
Rule #3: A final zero or trailing zero in the decimal portion ONLY are significant.

25. Practice Problems
How many significant digits are in each of the following examples?
1) 47.1
2) 9700 3)
4) 560 5) 6) 7) 8) 9)
10)
Answers: 3 2 7 6 4 5 1

26. Sig Figs in Calculations
When you +, -, ×, or ÷, your answer should only be as precise as the least precise measurement in the calculation.

27. Determining Significant Digits When Rounding
689.7
0.0072
4000
4 x 10-1
8800
309.00
7) .105
1) grams (4 significant digits) 2) (2 significant digits) 3) 4009 (1 significant digit) 4) x 10-1 (1 significant digit) 5) 8792 (2 significant digits) 6) (5 significant digits) 7) (3 significant digits)