1. Writing large and small numbers
Scientific Notation
Writing large and small numbers

2. It’s easy to make mistakes when computing with small numbers such as 0
It’s easy to make mistakes when computing with small numbers such as and large numbers such as 75,000,000. People who deal regularly with such numbers use scientific notation.
Scientific notation – a method of writing very large and very small numbers using powers of 10.
Take for example, an ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about centimeters across

3. Written in scientific notation:
Number of atoms in a penny;
2.0 x 1022
Size of each atom:
3.0 x 10-8
The sign on the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.

4. Writing Scientific Notation
Scientific notation is written using the product of 2 factors.
1.0 x 106 = 1,000,000
First factor is a number ≥ 1 but < 10.
1,000,000 = 1.0
Second factor is a power of 10 = (106)

5. Scientific Notation to Standard Notation
Write each number in standard notation.
2.64 x 107
2.64 x 10,000, = 10,000,000
26,400,000 Think: Move the decimal right 7 places for positive exponent.
1.35 x 10-4
1.35 x 1/10, = 1/10,000
Think: Move the decimal left 4 places for negative exponent.

6. Standard Notation to Scientific Notation
Write each number in scientific notation.
2 Move the decimal to get a number between 1 and 10
2 x 10□ Set up scientific notation. Think: decimal needs to move left 6 places to change 2 to , moving left makes exponent negative.
2 x 10-6
0.0027
2.7 Move the decimal to get a number between 1 and 10
2.7 x 10□ Set up scientific notation. Think: decimal needs to move left 3 places to
change 2.7 to , moving left makes exponent negative.
2.7 x 10-3

7. Scientific Notation with a Calculator
Technology Lab with TI-83
calculator

8. Scientist often have to work with very large or very small numbers
Scientist often have to work with very large or very small numbers. For example, the Andromeda Galaxy contains over 200,000,000,000 (billion) stars. Scientific notation is a compact way of expressing these numbers.
Show 200,000,000,000 in scientific notation on your graphing calculator.
Enter 200,000,000,000 on your calculator. Press
[ENTER]

9. 2E11 on the graphing calculator display means 2 x 1011
Your calculator automatically puts very large numbers into scientific notation.

10. Enter 2 x 1011 by pressing 2 [2nd] EE [,] 11 [enter]
You can enter scientific notation directly into the calculator yourself using the EE function key (2nd key then comma , key).
Enter 2 x 1011 by pressing 2 [2nd] EE [,] 11 [enter]

11. Evaluating Expressions using Scientific Notation
Evaluate 230,000,000 x 650,000
First write 230,000,000 in scientific notation = 2.3 x 108
Second write 650,000 in scientific notation = 6.5 x 105
Press 2.3 [2nd] EE [,] 8 x 6.5 [2nd] EE [,] 5 [enter]
In scientific notation, 230,000,000 x 650,000 is equal to x 1014 or 149,500,000,000,000
(149 trillion, 500 billion).

12. Write each number in scientific notation. 340,000,000,000 = 3.4 x 1011
Evaluate (340,000,000,000 ÷ 1,235) x 4,568
Write each number in scientific notation.
340,000,000,000 = 3.4 x 1011
1,235 = x 103
4,568 = x 103
Press (3.4 [2nd] EE [,] 11 ÷ [2nd] EE [,] 3 ) x [2nd] EE [,] 3 [enter]
(340,000,000,000 ÷ 1,235) x 4,568 =
x 1012
(because this calculator displays results to only 10 decimal places, this in not exact. The exact answer is x 1012)

13. Problem Solving
In space, light travels about 9,460,000,000,000 kilometers per year. This distance is known as a light-year. The star Altair is 16.3 light-years from earth. Write this distance in scientific notation.
Suppose the universe is made up of 125,000,000,000 galaxies, each containing 200,000,000,000 stars. Use this data to find the total number of stars in the entire universe. Express your answer in scientific notation and in standard form.

14. Answer (check out what these would look like in standard notation)
1.54E14 kilometers from earth
2.5E22 star in the universe

15. 25 sextillion stars in the universe
154,000,000,000, trillion kilometers
25,000,000,000,000,000,000,000
25 sextillion stars in the universe

16. Extremely small numbers are written in the same way but use (-) negative exponents.
For example, our ordinary penny contains about 20 sextillion atoms, written:
2.0E22 or 20,000,000,000,000,000,000 atoms
The average size of the atom we discussed earlier is about 3 hundred millionths centimeters across, written:
3.0E-8 or centimeters

17. The sign of the exponent tells which direction to move the decimal.
Helpful Hint
The sign of the exponent tells which direction to move the decimal.
A positive exponent means to move the decimal to the right.
A negative exponent means move the decimal to the left.

18. (5 septillion, 980 sextillion)
Math Fact !!!!!
The mass (weight) of the earth is about 5,980,000,000,000,000,000,000,000 kilograms.
(5 septillion, 980 sextillion)
This is written in scientific notation as
5.98 x 1024
How would you enter this into your calculator?

19. Ever wonder what 1 million pennies looks like? Here’s your answer.