1. Warm up – August 14, 2017
How many significant digits are in the following numbers and what are they?
Number
Sig fig
Which ones 81
26.2
0.007
380.0
78800
78800.

2. Warm up – August 14, 2017
How many significant digits are in the following numbers and what are they?
Number
Sig fig
Which ones 81 2
8,1
26.2 3
2,6,2
0.007 1 7 6
5,2,0,0,3,8
380.0 4
3,8,0,0
78800
7,8,8
78800. 5
7,8,8,0,0

3. Monday, August 14, 2017 Turn in homework Check sig fig foldable
Notes on Scientific notation & dimensional analysis
Scientific notation foldable
Dimensional analysis homework

4. Interactive Notebook Table of Content
Left Side
Page
Right Side
Scientific notation foldable 14
Scientific notation & dimensional analysis notes 15
Why is scientific notation used?

5. Scientific notation
Scientific notation is used to express very large or very small numbers
2 parts
Number between 1 and 10
x 10 to an exponent
The exponent can be determined by the number of decimal places you have to move to get only 1 number in front of the decimal

6. Large Numbers
If starting number is greater than 1 the exponent will be positive.
Example: (steps)
Move decimal until 1 number is in front:
Now add x10: x 10
Now count the number of decimal places that you moved: 4
Since number is greater than 1 the exponent will be positive : x 104

7. Small numbers
If the number you start with is less than 1, the exponent will be negative.
Example:
Move decimal until 1 number is in front: 5.2
Now add x10: 5.2 x 10
Now count the number of decimal places that you moved: 3
Since number is less than 1 the exponent will be negative: x 10-3

8. Going from Scientific notation to standard notation
You start with the number and move the decimal the same number of spaces as the exponent.
If the exponent is positive, the number will be greater than 1
If the exponent is negative the number will be less than 1.
Example: 3 x 106
5 x 10-4

9. Dimensional analysis
When we measure something, we always specify what units we are measuring in.
All kinds of units are possible, but in science we use the SI system
Problem! What if I measure something in inches but I am supposed to give you the answer using SI units?

10. Converting between different standards of measurement
How many seconds are in a day?
How many inches are in a centimeter?
If you are going 50 miles per hour, how many meters per second are you traveling?
To answer these questions you need to change (convert) from one unit to another.

11. How do you change units?
Whenever you have to convert a physical measurement from one dimensional unit to another, dimensional analysis is the method used.
Dimensional analysis – converting from one unit system to another.

12. How does dimensional analysis work?
In order to perform any conversion, you need a conversion factor.
Conversion factors are made from any two terms that describe the same or equivalent “amounts” of what we are interested in.
Examples:
1 inch
2.54 cm
1 miles
5,280 feet
60 minutes
1 hour
24 hours
1 day
100 cm
1 m
12 inches
1 foot
16 ounces
1 pound

13. Steps of dimensional analysis (copy step in INB)
All dimensional analysis problems are set up the same way. They follow this same pattern:
Identify starting and ending units
Line up conversion factors so units cancel
Multiply all top numbers and divide by each bottom number
Check units and answer
What units you have x What units you want = What units you want
What units you have
The units you want to end with
The number & units you start with
The conversion factor
(The equality that looks like a fraction)

14. Example Problem
How many feet are in 60 inches
You need a conversion factor. Something that will change inches into feet.
Remember
12 inches = 1 foot
Written as an “equality” or “ratio” it looks like
60 inches
5 feet x =
(Mathematically all you do is: 60 x 1  12 = 5)
What units you have x What units you want = What units you want
What units you have

15. Example Problem #2
You need to put gas in the car. Let's assume that gasoline costs $3.35 per gallon and you've got a twenty dollar bill. How many gallons of gas can you get with that twenty? Try it!
$ gallon = gallons
$ 3.35
(Mathematically all you do is: 20 x 1  3.35 = 5.97)

16. Example Problem #3
You have a twenty dollar bill and you need to get gas for your car. If gas is $3.35 a gallon and your car gets 24 miles per gallon, how many miles will you be able to drive your car on twenty dollars? Try it!
$ gallon miles = miles
$ gallon
(Mathematically all you do is: 20 x 1  3.35 x 24  1 = )

17. Scientific notation foldable