1. Scientific Notation

2. Objectives Express numbers in scientific notation.
Convert from standard form to scientific notation.
Convert from scientific notation to standard form.
Add, Subtract, Multiply, and Divide with scientific notation.

3. Scientific Notation Intro

4. Scientific Notation Consists of two parts 2. characteristic
1. mantissa
The full size number that comes before x 10
2. characteristic
The exponent that comes after x 10 and is superscript

5. Mantissa Characteristic
Scientific Notation
Example:
3.00 x 1015
Mantissa Characteristic

6. Scientific Notation
To convert a normal number to scientific notation, move the decimal either to the left or right until you have a mantissa which is greater than -10 or less than +10

7. Scientific Notation
If the absolute value of the number is smaller than 1, the characteristic will be negative
If the absolute value of the number is larger than 1, the characteristic will be positive

8. Moved to the left two spaces
Scientific Notation
Example:
542
The absolute value of the number is greater than one so the characteristic is positive
Moved to the left two spaces
5.42 x 102

9. Moved to the left seven spaces
Scientific Notation
Example:
The absolute value of the number is greater than one so the characteristic is positive
Moved to the left seven spaces
-4.5 x 107

10. Moved to the right three spaces
Example:
0.0040
The absolute value of the number is less than one so the characteristic is negative
Moved to the right three spaces
4.0 x 10-3

11. Moved to the right one space
Example:
-0.209
The absolute value of the number is less than one so the characteristic is negative
Moved to the right one space
-2.09 x 10-1

12. Example:
9.245
The absolute value of the number is between -10 and +10.
The decimal is not moved. In this case, the characteristic is zero.
9.245 x100

13. Expanding Scientific Notation to Regular notation
If the characteristic is positive, move the decimal to the right.
If the characteristic is negative, move the decimal to the left.

14. Expanding Scientific Notation to Regular notation
Example
6.50 x 102
The characteristic tells us to move two places to the right.
650.

15. Expanding Scientific Notation to Regular notation
Example
6.50 x 10-2
The characteristic tells us to move two places to the left.
0.0650

16. Fixing Incorrect Scientific Notation
Fix the mantissa by moving the decimal
Add the “fixed” characteristic to the original characteristic

17. Moved over one space to the left (+) to correct the mantissa
Example
20.4 x 106 (incorrect)
Moved over one space to the left (+) to correct the mantissa
2.04 x 10(6+1)
2.04 x 107 (correct)

18. Moved over two spaces to the left (+) to correct the mantissa
Example
200.4 x 10-6 (incorrect)
Moved over two spaces to the left (+) to correct the mantissa
2.004 x 10(-6+2)
2.004 x 10-4 (correct)

19. Moved over three spaces to the right (-) to correct the mantissa
Example
x 108 (incorrect)
Moved over three spaces to the right (-) to correct the mantissa
3.40 x 10(8 + -3)
3.40 x 105 (correct)

20. Moved over three spaces to the right (-) to correct the mantissa
Example
x 10-8 (incorrect)
Moved over three spaces to the right (-) to correct the mantissa
3.40 x 10( )
3.40 x (correct)

21. Adding and Subtracting Scientific Notation
The mantissa MUST have the same characteristic.
Then add or subtract the mantissa.
Finally correct the scientific notation if needed

22. Multiplying Numbers in Scientific Notation
Multiply the mantissas
ADD the characteristics together
Correct the number if the mantissas are +10 or greater/-10 or less.

23. Dividing Numbers in Scientific Notation
Divide the mantissas
Subtract the characteristic of the denominator from the characteristic of the numerator
Correct the number if the mantissas are +10 or greater/-10 or less.