1. Scientific notation and Dimensional Analysis Mr. Conkey Fall Semester
Astronomy
Scientific notation and Dimensional Analysis
Mr. Conkey Fall Semester

2. Scientific Notation
Scientific notation is typically used when dealing with very large quantities or numbers as well as very small ones
It is useful because it expresses those amounts without having to enter the whole number into a calculator
Example: If I had a sample of 350,000,000 (three hundred-fifty million in standard notation) microscopic meteorites, the number expressed in scientific notation would be 3.5 x 10 ⁸ meteorites

3. Scientific Notation Rules
The Rules –
3.5 is the base number and MUST be between 1 and 10 (this tells you where to move the decimal point to).
x 10 is your power of 10 you are multiplying the base number by
⁸ is the exponent (how many powers of 10 you are multiplying by)
For large numbers, when going from standard notation to scientific, you would move the decimal to the left which ALWAYS gives a positive exponent
3.5
x 10 ⁸

4. Scientific notation rules (Cont.)
When working with numbers less than one and converting from standard to scientific notation, you would move the decimal to the right which ALWAYS gives you a negative exponent
“How do I know what my exponent should be?”
This depends on how many times you have to move the decimal place in order to make the base number between 1 and 10

5. Standard to Scientific notation examples
Example: convert 584,200. grams to scientific notation
The arrows show how many times the decimal point moves to the left, giving us
x 105
Example: convert grams to scientific notation
The arrows show how many times the decimal point moves giving us
5.46 x 10 ˉ³ grams

6. Lets try some…
245,385
0.013
385
0.193
5.9
x 105
1.3 x 10ˉ2
3.85 x 102
1.93 x 10ˉ1
5.9 x 100

7. Going back to Standard notation
In order to convert from scientific notation to standard, you would move the decimal place in the OPPOSITE direction than before
Example 1: convert x 104 to standard notation
The 4 tells us we need to move the decimal four times to the right
In order to do this, we have to add a zero to the right side =
This gives us 54,620.

8. Going back to Standard Notation (cont.)
Example 2: convert x 10ˉ2 to standard notation
The ˉ2 tells us we need to move the decimal place two times to the left
To do this, we add one zero to the left side =
This gives us

9. Lets do this!!!
1.893 x 105
x 10ˉ3
5.32 x 100
x 107
x 105
189,300
5.32
98,372,000
This one is tricky! The correct scientific notation for this is x 104 because of the decimal being in the wrong spot (remember the between 1 and 10 rule!); therefore the standard notation is 1,569.2

10. Shifting gears: Dimensional analysis
Dimensional analysis is used to compare one thing to another using a fundamental unit (i.e. grams, liters, meters, etc.)
In order to do this, you must first know the conversion factors to use:
1000 base units = 1 kilo-
10 of these = 1 base unit
100 of these = 1 base unit
1000 of these = 1 base unit

11. Dimensional analysis examples (single and multiple steps)
Example: Convert 1500 centimeters (cm) to meters (m)
When setting up the table, you begin with the given number and unit in the upper left
Next, look up how many cm in 1 m on the conversion ladder and put this number in the lower right
Finally, put the 1 m in the top right
1500 cm
1 m
Multiply the top
100 cm
Divide the Bottom
= 15 m

12. Dimensional analysis examples (single and multiple steps(cont.))
Example: Convert centigrams (cg) to kilograms (kg)
This is similar to the last example except there will be multiple conversions in the table
2630 cg
1 g
1 kg
100 cg
1000 g
= kg