1. Scientific Notation

2. Scientific Notation Why do we use scientific notation?
Because in science we often deal with numbers which are
ridiculously large or unimaginable small.
For example:

3. Scientific Notation How many stars are in an average spiral galaxy?
Answer: At least 200 Billion stars. or
200,000,000,000,000 stars.

4. Scientific Notation
What is the distance between the electron and the nucleus of
an atom?
Answer: meters.

5. Scientific Notation
It is not practical for us to work with numbers written as:
200,000,000,000 or
So, we have come up with a way of dealing with these large
and small numbers.
And its called…
Scientific Notation.

6. Correct Scientific Notation
M x 10n
Exponent (Order of Magnitude)
+ Positive for numbers greater than 1
- Negative for numbers less than 1
Mantissa
A number from one to less than ten.
Ex: 1.3, 3.4, 5.26

7. Scientific Notation Converting Large numbers to Scientific Notation.
Example:
1,500,000 m
Mantissa = 1.5
Exponent = 6, for 6 decimal places, and positive
1.5 x 106 m

8. Scientific Notation Converting Small numbers to Scientific Notation.
Example: A
Mantissa = 2.5
Exponent = -5, 5 for 5 decimal places, and negative A

9. Scientific Notation
The following two numbers are equal, however only one is expressed correctly. Which one?
17.5 x 105 m = 1.75 x 106
Answer: 1.75 x 106 m,
the mantissa is a number from

10. Scientific Notation Special Case No. 1: 1 1 x 100 = _______
Remember, the exponent tells us how much to move the decimal.
In this case the exponent is zero. So, the decimal remains where it is.

11. Scientific Notation Special Case No. 2: 10 1 x 101 = _______
101 is like writing a word in shorthand or an abbreviation.
It is implied that there is a “1 x” before the 101.

12. Scientific Notation Convert the following to scientific notation.
5.0 x 10-3
2.5 x 10-1
0.005 = ______________
0.25 = _______________
5.050 x 103
2.5 x 10-2
5,050 = ______________
0.025 = ______________
8 x 10-4
2.5 x 10-3
= _____________
= _____________
1 x 103
500 = _______________
5 x 102
1,000 = ______________
1 x 106
5,000 = ______________
5 x 103
1,000,000 = __________

13. Scientific Notation Convert the following to standard notation. 1,500
.335
1.5 x 103 = __________________
3.35 x 10-1 = __________________
.0015
.00012
1.5 x 10-3 = ____________
1.2 x 10-4 = _____________
.0375
10,000
3.75 x 10-2 = _________________
1 x 104 = _______________________ .1
375
1 x 10-1 = ________________________
3.75 x 102 = ___________________
220,000
4 x 100 = _______________ 4
2.2 x 105 = ____________________

14. Homework Answers Part B 1) 1,000,000 2) .00001 3) 100,000,000,000
Part A
1) 104
2) 10-3
3) 108
4) 3 x 107
5) 4.35 x 1011
6) 1.09 x 108
7) 6.78 x 107
8) 9 x 103
9) 6.02 x 10-1
10) 2.3 x 10-5
11) 5.43 x 101
12) 5.60 x 10-10
Part B
1) 1,000,000 2)
3) 100,000,000,000
4) .0004 5)
6) 823,000,000 7)
8) 7,680 9)
10) 2.85
11) 9,680,000,000,000
12)