1. Objective The student will be able to: express numbers in scientific and decimal notation.

2. Scientific Notation is used to express the very large and the very small numbers so that problem solving will be made easier. Examples: The mass of one gold atom is.000 000 000 000 000 000 000 327 grams. One gram of hydrogen contains 602 000 000 000 000 000 000 000 hydrogen atoms. Scientists can work with very large and very small numbers more easily if the numbers are written in a short notation called scientific notation.

3. Scientific Notation A short way to express very large and very small numbers. A number expressed in Scientific Notation is in the following form: a x 10 n where a is 1 or a number between 1 and 10 & n is an integer (positive or negative)

4. Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number 1 or a number between 1 and 10? Between the 2 and the 1 (after the very first number ALWAYS)

5. 2. 10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 10 23

6. Now, Express 0.0000000902 in scientific notation. Where would the decimal go to make the number between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10 -8

7. Practice Problems Put these numbers in scientific notation. 1).00012 2) 1000 3) 0.01 4) 12 5).987 6) 596 7).000 000 7 8) 1,000,000 9).001257 10) 987,653,000,000 11) 8 PROBLEMS 1) 1.2 x 10 -4 2) 1 x 10 3 3) 1 x 10 -2 4) 1.2 x 10 1 5) 9.87 x 10 -1 6) 5.96 x 10 2 7) 7.0 x 10 -7 8) 1.0 x 10 6 9) 1.26 x 10 -3 10) 9.88 x 10 11 11) 8 x 10 0 1) 1.2 x 10 -4 2) 1 x 10 3 3) 1 x 10 -2 4) 1.2 x 10 1 5) 9.87 x 10 -1 6) 5.96 x 10 2 7) 7.0 x 10 -7 8) 1.0 x 10 6 9) 1.26 x 10 -3 10) 9.88 x 10 11 11) 8 x 10 0 ANSWERS

8. EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS PROBLEMSANSWERS 1) 4.9 X 10 2 2) 3.75 X 10 -2 3) 5.95 X 10 -4 4) 9.46 X 10 3 5) 3.87 X 10 1 6) 7.10 X 10 0 7) 8.2 X 10 -5 1)490 2).0375 3).000595 4)9460 5)38.7 6)7.10 7).000082

9. Scientific Notation and The TI-84 Plus On the graphing calculator, scientific notation can be computed by using the EE (2 ND Comma) button. Therefore, 4.58 x 10 6 is typed 4.58 E 6 on the Graphing Calculator. This is because E means (times 10 / X 10)

10. Scientific Notation Part 1 is OVER!!! You are ready to move on to the investigation!

11. Use a calculator to evaluate: 4.5 x 10 -5 1.6 x 10 -2 Type 4.5E-5 1.6 E -2 You must include parentheses if you don’t use those buttons!! (4.5 x 10 -5) (1.6 x 10 -2) 0.0028125 Write in scientific notation. 2.8125 x 10 -3

12. 5) Use a calculator to evaluate: 7.2 x 10 -9 1.2 x 10 2 On the calculator, the answer is: 6.E -11 The answer in scientific notation is 6 x 10 -11 The answer in decimal notation is 0.00000000006

13. 6) Use a calculator to evaluate (0.0042)(330,000). On the calculator, the answer is 1386. The answer in decimal notation is 1386 The answer in scientific notation is 1.386 x 10 3

14. 7) Use a calculator to evaluate (3,600,000,000)(23). On the calculator, the answer is: 8.28 E +10 The answer in scientific notation is 8.28 x 10 10 The answer in decimal notation is 82,800,000,000

15. Write (2.8 x 10 3 )(5.1 x 10 -7 ) in scientific notation. 1.14.28 x 10 -4 2.1.428 x 10 -3 3.14.28 x 10 10 4.1.428 x 10 11

16. Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) 234.6 x 10 9 2.346 x 10 11 9) 0.0642 x 10 4 on calculator: 642 6.42 x 10 2

17. Write 531.42 x 10 5 in scientific notation. 1..53142 x 10 2 2.5.3142 x 10 3 3.53.142 x 10 4 4.531.42 x 10 5 5.53.142 x 10 6 6.5.3142 x 10 7 7..53142 x 10 8