1. Scientific Notation & Units
Problem Solving
Scientific Notation & Units
Section 5.1 & 5.3A
Period #6
Group #3

2. This cartoon explains the importance of numbers & units today.
Background
Measurements such as “fathom,” “rod,” and “cubit” were inaccurate units of measurements used in the past.
Side Note: NASA sent a $125 million dollars spacecraft off–course on its way to Mars due to use of English units instead of metric. This is a cartoon that is based off NASA’s blunder and which demonstrates NASA’s confusing directions.
This cartoon explains the importance of numbers & units today.

3. Peanuts Background Cartoon

4. Scientific Notation
Scientific Notation: expresses a number as a product of a number between 1 & 10 and the appropriate power of 10
Purpose: to express a large or small quantity without using many unnecessary zeros

5. Conversion of Large Numbers  Scientific Notation
1. Number in standard notation
2. Add a decimal after last digit
3. Move decimal to the left (only 1 digit left in front)
4. Cross out zeros at the end
5. Rewrite # as the decimal multiply it by
10^(# of times you moved the decimal to the left)

6. Conversion of Small Numbers  Scientific Notation
Number in standard notation
Move the decimal to the right  until it goes past the first non-zero digit
Cross out the zeros in front
Rewrite the number and multiply it by
10^(# of times you moved the decimal the right)

7. Example
Q: Explain the error in the following conversion. Write the correct scientific notation.
 21.7 x 10-4
A: The error is that scientific notation expresses a product of a power between 1 & 10 and the appropriate power of 10. In this case, 21.7 is not a number between 1 and 10. The correct scientific notation is 2.17 x 10-3.

8. Units Unit: the part of the measurement that
tells us the scale/standard being used
(quantitative part of measurement)
Used by
Examples
Metric System
*SI unit based on Metric System
Most of the world
Meters, grams, kilometers, centimeters, liters
English system
United States
Pounds, ounces, cups, feet, inches, miles
This cartoon expresses the importance of units and describes the difficulty with two measurement systems.

9. Commonly Used Prefixes in the Metric System
Units
Common Fundamental SI Units
Quality
Name of Unit
Abbreviation
Mass
kilogram kg
Length
meter m
Time
second s
Temperature
kelvin K
Commonly Used Prefixes in the Metric System
Prefix
Symbol
Meaning
Power of 10
Mega M
1,000,000
106
Kilo k
1000
103
Deci d
0.1
10-1
Centi c
0.01
10-2
Milli m
0.001
10-3
Micro
10-6
Nano n
10-9
Because fundamental units are not always a convenient size, the SI system uses prefixes to change the size of the unit to accommodate them.

10. Example Q: Why are prefixes such as mega,
kilo-, deci-, centi-, milli-, etc. needed?
A: Because fundamental units are not
always a convenient size, the SI system
uses prefixes to change the size of the unit
to accommodate them.

11. Measurements of Length, Mass, & Volume
Length – the distance of an object measured end to end
SI unit of length is meter
Volume – amount of 3D space occupied by a substance (length x width x height)
SI unit is the cubic meter (m3)
Liquids are measured in liters (dm3) & millimeters (cm3)
Mass – a quantity of matter present in an object
Metric unit is gram
SI unit is kilogram

12. Measurements of Length, Mass & Volume
Commonly Used Metric Units for Length
Unit
Symbol
Equivalence
Kilometer km
1000m
Meter m
1 m
Decimeter dm
0.1m
Centimeter cm
0.01 m
Millimeter mm
0.001m
Commonly Used Metric Units for Volume
Unit
Symbol
Equivalence
Liter L
1L = 1000 mL= 1 dc3
Milliliter mL
1 mL = 0.001L = 1 cm3
Commonly Used Metric Units for Mass
Unit
Symbol
Equivalence
Kilogram kg
1 kg = 1000 g
Gram g
1 g
Milligram mg
1 mg = g

13. Measurements of Length, Mass, & Volume
1kg = 1000g
1mg = 0.001g
1g = 1000mg

14. Example Q: How does a kilometer compare
to a meter? How does a milliliter compare to a liter?
A: A kilometer is 1000 meters while a milliliter is liter.

15. Problem Solving Problem Solving Ask yourself these questions…
Attack problem systematically:
Ask yourself these questions…
Where do we want to go?
What do we know?
How do we get there?
Does it make sense?
Problem Solving

16. Example
Q: What are some of the questions that could be used to arrive at a solution? A: Where do we want to go? What do we know? How do we get there? Does it make sense?

17. Unit Conversions Convert Units: 2. Choose the conversion factor
Dimensional Analysis – to convert one system of units to another by using conversion factors
Equivalence Statement - shows relationship between units of different systems
Ex: cm = 1 in.
Conversion Factor - are ratios of the 2 parts of the equivalence statement.
Ex: 2.54 cm or 1 in.
1 in cm
Steps to Find an equivalence statement that relates the 2 units
Convert Units: 2. Choose the conversion factor
3. Multiply the quantity by the conversion factor
4. Check to make sure you have correct # of significant factors

18. Unit Conversions
Picture includes multiple systems of measurements in equivalent statements.
A humorous cartoon which depicts the unit conversion when people travel to other countries.

19. Example Q: Define dimensional analysis in your own words.
A: Dimensional analysis is to change one system of units to another by using conversion factors.

20. Quiz on 5.1 & 5.3A Scientific Notation
Solve each of the following. Which of the two measurements is greater?
a.) x b.) x 102
Units
Are units the qualitative or quantitative part of a measurement? Explain?
Measurements of Length, Mass, & Volume
What is mass and its SI unit?
Problem Solving
Give an everyday example of how dimensional analysis has helped you in life.
Converting Units
What must we use to convert units?

21. Quiz Answers Scientific Notation Units
The value of A is 26,700 and the value of B is 28,700. Choice B is the greater value.
Units
Units are a quantitative part of a measurement because it describes the amount.
Measurements of Length, Mass, & Volume
Mass is the quantity of matter present in an object. Its SI unit is kilogram.
Problem Solving
(Answers will vary. Check if answers relate to converting units to achieve something.)
Converting Units
To be able to convert units, you must use an equivalence statement that relates the 2 different units in the equation. Then, you must turn the equivalence statement into a conversion factor to get the desired unit.

22. Sources Scientific Notation Explanation
Scientific Notation Exercises
(highly recommended)
Converting Units