1. Fun with numbers:
Scientific Notation

2. There are about 6 billion people on earth. That’s 6,000,000,000.
The number of cells in a person’s body is about 50 trillion. That’s 50,000,000,000,000.
The mass of a single proton is

3. How about this one? The sun contains about two decillion grams of hydrogen. 2,000,000,000,000,000,000,000, 000,000,000, with 33 zeroes after it!

4. That’s too much to work with
That’s too much to work with! That’s why we use scientific notation in chemistry. We use scientific notation to express numbers that are extremely large or extremely small.

5. Expressing in scientific notation: The form is N x 10x where N is a number greater than 1 but less than 10, and x is the exponent.

6. Which of these numbers is in scientific notation. A. 5. 0 x 103 B
Which of these numbers is in scientific notation? A x 103 B x 104
How do we know?
Because 5.0 is greater than 1, but less than 10 and 0.5 is not!

7. Putting numbers into scientific notation: 5,000,000
Move the decimal point behind the first number greater than 0. That number becomes your coefficient (but you can drop extra zeros).
The number of times you moved the decimal point becomes the exponent.
So 5,000,000 in scientific notation is 5.0 x 106

8. Practice: Convert 1,234,000,000 into scientific notation.
1.234 x 109

9. Scientific notation helps with small numbers too!

10. Scientific Notation of very small numbers
is 2 x 10-8
The “-” means the number in standard notation was less than one. We had to move the decimal to the right.

11. Let’s Practice 6400: ___________________________ 6.4 x 103
6400: ___________________________
: __________________
: ___________________
3,430,000,000,000: ________________
232,000: ________________________
: _______________________
6.4 x 103
4.52 x 10-8
5.6 x 10-6
3.43 x 1012
2.32 x 105
1.320 x 10-3

12. Scientific Notation to Standard Notation
If the exponent is positive, move the decimal point that many places to the right.
7.68 x 108 = = 768,000,000
If the exponent is negative, move the decimal point that many places to the left.
3.99 x 10-5 = =

13. Let’s Practice 6.41 X 10-11: _____________________ 0.000 000 000 064 1
105,000,000,000,000
98,700
50,800,000,000

14. Adding and Subtracting
Step 1: Adjust the powers of 10 in the 2 numbers so that they are the same.
(Tip: It is easier to adjust the smaller power to equal the larger power).
(Tip: One will not be in true scientific notation)
Step 2 : Add or subtract the numbers.
Step 3 : Give the answer in scientific notation.

15. = .20 x 10³ x 10³
2.0 x 10² ³
Step 1: Adjust the powers of 10 in the 2 numbers so that they are the same.
(Tip: It is easier to adjust the smaller power to equal the larger power).
(Tip: One will not be in true scientific notation)
Step 2 : Add or subtract the numbers.
Step 3 : Give the answer in scientific notation.
.2 x 10³ x 10³
= (.2+3) x 10³
= 3.2 x 10³
2.0 x x 105
2.0 x x 107
= ( ) x 107
= x 107
1. Make exponents the same
2. Subtract and keep the 107

16. Multiplying To multiply numbers in scientific notation:
Step 1 : Group the numbers together.
Step 2 : Multiply the numbers.
Step 3 : Add the powers of 10.
Step 4 : Give the answer in scientific notation.

17. 3x108 x 1.5x1023 =
Step 1 : Group the numbers together.
Step 2 : Multiply the numbers.
Step 3 : Add the powers of 10.
Step 4 : Give the answer in scientific notation.
(3x1.5)x(108+23)
=4.5x1031
4.0x108 x 5.0x106 =
(4.0x5.0) x =
20x1014
=2.0x1015

18. Dividing To divide numbers in scientific notation:
Step 1 : Group the numbers together.
Step 2 : Divide the numbers.
Step 3 : Subtract the powers of 10.
Step 4 : Give the answer in scientific notation.

19. 4.5x108
3x105
4.5 3
x 108-5
Step 1 : Group the numbers together.
Step 2 : Divide the numbers.
Step 3 : Subtract the powers of
Step 4 : Give the answer in scientific notation.
= 1.5x103

20. Practice makes perfect!
So let’s practice!