OBJECTIVE: Scientific Notation the art of writing very large numbers

1. OBJECTIVE: Scientific Notationthe art of writing very large numbers If it’s black, write it into your notes. Get out some paper and a pencil or pen NOW.

2. We can write numbers many ways. For example the number one can be written as 100.0 2002 100 • 1 x 102 All of these math expressions means that idea of “ONE” This last one is called Scientific Notation

3. We can write any number in scientific notation, but it makes much more sense to use it only for really, really big numbers (or really small ones). Let’s write these numbers in scientific notation 2,000,000 _________________________________ 4,500,000,000 _______________________________

4. Let’s write these numbers in scientific notation 2,000,000 = 2 x 106 4,500,000,000 = 4.5 x 109 The rule is always write the numbers as a coefficient:a decimal between 1.0 but less than 10. Then, count how many places you moved the invisible decimal and that’s how many times your power of ten should be.

5. Let’s try three more big numbers to scientific notation 55,000,000,000,000 ________________ 3,450,000,000 ___________________ 123,800,000 _____________________

6. Let’s try three more big numbers to scientific notation 55,000,000,000,000 = 5.5 x 1013 3,450,000,000 = 3.45 x 109 123,800,000 = 1.238 x 108

7. We’ve discussed the crazy big numbers of measurements like the distance of Neptune from the Sun. • That distance is 2,800,000,000 miles. • To say that number, we say: _________________________________________________ • That number: 2,800,000,000 mileshas an “INVISIBLE DECIMAL POINT” that I will add now • 2,800,000,000. miles • Write this distance in scientific notation.

8. 2,800,000,000. miles • is • 2.8 x 109 miles Now that we can, let’s do a bunch of these for practice. (ready?)

9. The distance between the Sun and the Earth is 93,000,000 miles ____________________ The distance between the Sun and Pluto is 4,800,000,000 miles ____________________ The diameter of the Sun is 870,000 miles _______________________ The number of water molecules in 1.0 liters of water is about 33,700,000,000,000,000,000,000,000 _____________________________

10. The distance between the Sun and the Earth is 93,000,000 miles 9.3 x 107 miles The distance between the Sun and Pluto is 4,800,000,000 miles 4.8 x 109 miles The diameter of the Sun is 870,000 miles 8.7 x 105 miles The number of water molecules in 1.0 liters of water is about 33,700,000,000,000,000,000,000,000 3.37 x 1025 molecules

11. Change these to scientific notation as well… 4,560,000,000,000,000,000 ants in New York ____________________________________ 3,400 pounds in a hippopotamus ______________________________ 6,000,000,000 years the Earth has bee around___________________________________

12. Change these to scientific notation as well… 4,560,000,000,000,000,000 ants in New York 4.56 x 1018 ants 3,400 pounds in a hippopotamus 3.4 x 103 pounds 6,000,000,000 years the Earth has bee around6 x 109 years

13. Every Power of Ten is 10X bigger than the last one… 101 = 1 x 10 = 10 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1000 104 = 10 x 10 x 10 x 10 = 10,000 105 = 10 x 10 x 10 x 10 x 10 = 100,000 106 = 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 107 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000