1. Scientific Notation *Used to describe numbers with the powers of 10. Used mainly with very large numbers and very small numbers. Large numbers (greater than 1) get positive exponents. Small numbers (less than 1) get negative exponents. Steps to write numbers in scientific notation: 1) move decimal to the right of the first nonzero number 2) write that number and the numbers to the right of it 3) write “ x 10” to a power (exponent) depending on how many times you moved the decimal in step #1 Examples: Write in scientific notation. 1) 472 = 4.72 x 10 2 2) 0.000045 = 4.5 x 10 -5

2. Whole Number Examples 723,000 7.23 x 10 5 Drop all zeros, and write the number of places the decimal point moved as a positive exponent. 7.23000 Move the decimal point to get a number greater than 1 but less than ten. 7.23000Count the places after the decimal.

3. Your Turn: Rewrite in Scientific Notation 212,000 302,000,000 2.12000 2.12 x 10 5 3.02000000 3.02000000 3.02 x 10 8

4. Decimal Number Examples 0.0052 5.2 x10 -3 Drop all zeros, and use the number of places the decimal point moved as with a negative exponent. 0.005.2 Move the decimal point to get a number greater than 1 but less than 10. 0.005.2 Count the places before the decimal.

5. Your Turn: Rewrite in Scientific Notation 0.000210.0002.1 0.0002.1 2.1 x 10 -4 0.000 000 459 0.000 000 4.59 0.000 000 4.59 0.000 000 4.59 4.59 x 10 -7

6. Examples: 1) 78000 2) 4,520,000 3) 0 0004 4) 0 00283 5) 128 6) 0 000000756 7.8 x 10 4 4 x 10 -4 7.56 x 10 -7 2.83 x 10 -3 1.28 x 10 2 4.52 x 10 6......

7. Try these: 1) 0.00482) 67,000,000 3) 45004) 0.000000526 5) 246) 0.92 4.8 x 10 -3 6.7 x 10 7 4.5 x 10 3 5.26 x 10 -7 2.4 x 10 1 9.2 x 10 -1

8. Un-doing Scientific Notation What is 8.6 x 10 6 in standard notation? Remember: –A positive exponent tells you how many places to move the decimal FORWARD. 8,600,000

9. A negative exponent tells you how many places to move the decimal BACKWARDS. What is 4.81 x 10 -5 in standard notation? Un-doing Scientific Notation 0.0000481

10. Write in Standard Notation 6.97 X 10 7 8 x 10 -6 9.807 x 10 5 3.2 x 10 -8 69,700,000 0.000008 980,700 0.000 000 032

11. Ordering Scientific Notation 6.4 x 10 6 3.21 x 10 4 5.8 x 10 6 Start by re-writing each number in scientific notation. 0.064 x 10 8 321 x 10 2 0.58 x 10

12. Ordering Scientific Notation Order the powers of ten and arrange the decimals with the same power of 10 in order 3.21 x 10 4 5.8 x 10 6 6.4 x 10 6 Change them back to the original numbers. 321 x 10 2 0.58 x 10 6 0.064 x 10 8

13. Your Turn Put these in order from smallest to largest 526 x 10 7 18.3 x 10 6 0.098 x 10 9 5.26 x 10 9 1.83 x 10 7 9.8 x 10 7 18.3 x 10 6 0.098 x 10 9 526 x 10 7 18.3 x 10 6 0.098 x 10 9 526 x 10 7 1.83 x 10 7 9.8 x 10 7 5.26 x 10 9

14. Calculating with Scientific Notation (3 x 10 -7 ) x (9 x 10 3 ) Use the commutative property 3 x 9 x 10 3 x 10 -7 3 x 9 x 10 3 x 10 -7 Multiply 3 x 9 and add the exponents 27 x 10 -4 27 x 10 -4 Rewrite in scientific notation 2.7 x 10 -3

15. Practice Complete page 212 #1-13 BE SURE TO READ ALL YOUR NOTES!