1. Scientific Notation: A Review Physics 1 st 6wks

2. How wide is our observable universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal or standard notation. When numbers get this large, it is easier to write them in scientific notation.

3. Scientific Notation

4. Write the width of the universe in scientific notation.

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. 1) Express 0.0000000902 in scientific notation.

7. Write 28750.9 in scientific notation. 1.2.87509 x 10 -5 2.2.87509 x 10 -4 3.2.87509 x 10 4 4.2.87509 x 10 5

8. 2) Express 1.8 x 10 -4 in decimal (aka “standard”) notation. 0.00018 3) Express 4.58 x 10 6 in decimal notation. 4,580,000 On the graphing calculator, scientific notation is done by hitting the button then the button (some have their own button 4.58 x 10 6 is typed 4.58 6

9. Scientific Notation on the Screen When you use the EE feature to input the “x 10” portion of a scientific notation value in calculator it will be displayed as Which correctly depicts 0.016 or 1.6 x 10 -2 You can also type “10^” symbol in the calculator to replace the “x 10” portion and see this instead (but that’s up to you) However if you used the ^ symbol by itself, and say this You really typed 0.390625 instead of 0.016

10. 4) Use a calculator to evaluate: 4.5 x 10 -5 1.6 x 10 -2 Type 4.5 -5 1.6 -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

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

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

13. 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/standard notation is 82,800,000,000

14. 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

15. 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 6.42 x 10 2

16. 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

17. Going from scientific notation to decimal/standard notation – with a positive exponent When you see a number in scientific notation like 9.87 x 10 4 the exponent will tell you how many times to move the decimal to the right to put it back into decimal notation The positive exponent means the number is a “large number”, that is one that is not less than one. Therefore 9.87 x 10 4 is equal to 98700

18. Write 8.04 x 10 5 in decimal notation. A.804 B.8040 C.80400 D.804000 E.8040000

19. Going from scientific notation to decimal notation – with a negative exponent When you see a number in scientific notation like 9.87 x 10 -4 the exponent will tell you how many times to move the decimal to the left to put it back into decimal notation The negative exponent means it is a “small” number, that is a number less than one. Therefore 9.87 x 10 -4 is equal to 0.000987

20. Write 8.04 x 10 -2 in decimal notation. A.804 B.80.4 C.0.804 D.0.0804 E.0.00804

21. An interesting situation… When you see a number in scientific notation like 9.87 x 10 0 The zero exponent means that the decimal point is not moved at all. Therefore 9.87 x 10 0 is equal to 9.87 There will virtually never be a reason why we would do that in Physics since we use Scientific Notation to express large numbers (especially those with large amounts of zeroes) in smaller, more manageable forms, but its cool to know it anyway!