1. Scientific Notation
Scientific Notation is a number written as the product of 2 numbers: a coefficient and 10 raised to a power.
This is useful for writing very large or very small
numbers.

2. RULES For Scientific Notation
1. Rewrite your number where there is just 1 non-zero digit with a decimal to the right.
2. Then count the number of spaces the decimal was moved and write that as an exponent.

3. RULES For Scientific Notation
3. If the original number is greater than one, the exponent is positive.
4. If the original number is less than one, the exponent is negative.

4. Converting to Scientific Notation
Example #1:
1. Find Decimal
Point.
– 36,000 .
Move decimal directly behind the first NON-ZERO number.
Count the number of spaces
decimal moved.

5. Converting to Scientific Notation
36,000
Example #1 Continued:
–Write the number with the new
location of decimal. 3.6
–Add x10 to the end of the new
number.
3.6 x 10

6. Converting to Scientific Notation
36,000
Example #1 Continued:
–How many spaces did you move the
decimal?
4 spaces
–This number becomes the exponent.
3.6 x 10 4
–Is the original number greater or less
than 1?
greater

7. Converting to Scientific Notation
36,000
Example #1 Continued:
–Since 36,000 greater than 1, the
exponent will be positive.
–Answer:
3.6 x 10 4

8. Converting to Scientific Notation Example #2: 0.000403 ==
4.03 X 10 -4

9. Expanding Scientific Notation
If the exponent is positive, move the decimal to the right.
If the exponent is negative, move the
decimal to the left.
Examples:
– 2.6 x 104 = –
1.08 x 10‒5 =

10. Practice
Write in Correct Scientific Notation
• 6,378,000
6.37 x 106 •
1.54 x 10‒10
• 91.4 x 104 •
9.14 x 105
8 x 10‒6
• 4.67
4.67 x 100

11. Practice
Expand to Standard Notation
• 4.5 x 105
• 7.38 x 10‒3
• 2.19 x 100
• 4.92 x 108
• 5.3 x 10‒7

12. Calculator Input Entering Scientific Notation into Calculator
Graphing Calculator:
Enter coefficient
Press 2nd button
Press comma key (an E should
appear on screen)
Enter exponent.

13. Calculator Input Entering Scientific Notation into Calculator
Scientific Calculator:
Enter coefficient
Press 2nd button
Press x–1 (an E should appear on
screen)
Enter exponent.

14. Calculator Input Continue
–Guidelines:
NEVER type in ‘ x10^ '
Use the (-) sign by the decimal place for negative exponents. NOT the subtraction key.
Follow Addition/Subtraction and Multiplication/Division Significant Figures Rules to determine how to round answers.

15. Calculator Practice First, make sure calculator is in SCI mode.
–Graphing Calculator:
MODE, SCI, Enter, Clear
–Scientific Calculator:
Push 2nd, DRG, SCI, Enter

16. Calculator Practice
Perform operations in the calculator. Round answer to the correct number of Significant Digits/Decimal Places.
1.35 x x 105 — 5.2 x 10‒16 =
Add/Subtract: Count numbers decimal places.
Answer = 4.3 x 105
(6.42 x 10‒2) ÷ (9.2 x 10‒5) =
Multiply/Divide: Count numbers sig. figs.
Answer = 7.0 x 102

17. Practice