1. BIG NUMBERS and SMALL NUMBERS (Scientific Notation)

2. In science, you sometimes have to deal with very LARGE numbers How far is the sun from the earth?

3. 150,000,000,000 meters

4. Or there may be times that you’ll use very small numbers… How wide is one atom of gold?

5. 0. 000 000 000 274 meters

6. Scientific notation is a system used to avoid dealing with all the ZEROS in very big and very small numbers

7. In scientific notation, numbers have TWO parts n { a number between 1-10 that may be followed by decimals} X 10 x a power of 10

8. How do you write numbers in scientific notation?

9. Problem Write 150,000,000,000 in scientific notation: Step 1 Move the decimal point from its original position until it is behind first nonzero digit (1). This gives you a number between 1 and 10. 150 000 000 000. From here To here The number becomes 1.5

10. Step 2 Count the number of places that the decimal point moves to the left; this becomes the positive exponent 150 000 000 000. (The decimal pt. moves 11 places; the exponent of 10 must be 11) Answer: 1.5 x 10 11

11. As you can see, there are two ways to write the SAME number 150 000 000 000 (standard notation) or 1.5 x 10 11 (scientific notation)

12. Problem: Write 0.000 000 000 274 in scientific notation Step 1 Move the decimal point from its original position until it is behind first nonzero digit (2). This gives you a number between 1 and 10. 0.000 000 000 274 From here To here The number becomes 2.74

13. Step 2 Count the number of places that the decimal point moves to the right ; this becomes the negative exponent 0.000 000 000 274 (The decimal pt. moves 10 places; the exponent of 10 must be 10) Answer: 2.74 x 10 -10

14. Again, there are obviously two ways to write this small number. 0.000 000 000 274 (standard notation) or 2.74 x 10 -10 (scientific notation)

15. Remember Big numbers have positive exponents Small numbers have negative exponents

16. Now let’s practice ! Write 45 880 000 in scientific notation. Correct answer is: 4.588 x 10 7

17. Let’s try another one… Write 0.000 005 397 in scientific notation. Correct answer is: 5.397 x 10 -6

18. You’re on your own… Write these numbers in scientific notation: (1) 6,700 (2) 123,000 (3) 0.0089 (4) 9,362,000 (5) 0.000 008 75

19. One more thing Be sure you also know how to change a number in scientific notation back to standard form. For example: Scientific notation: 8.32 x 10 4 How do you write this number in standard form? Answer: Standard form: 83 200

20. How do you change numbers in scientific notation to standard form?

21. Big numbers For numbers with positive exponents For numbers with positive exponents Move the decimal point from its current position to the right. The number of decimal places moved must be the same as the exponent. Fill the spaces with zeros. 6.33 x 10 5 From here …. move decimal point 5 places to the right (you need to write 3 zeros) Answer: 633 000

22. Shall we give it a try? Change 5.02 x 10 6 to standard form 5.02 x 10 6 Move the decimal point 6 places to the right You will need to write in 4 more zeros Answer: 5020000 or 5 020 000

23. Small numbers For numbers with negative exponents Move the decimal point from its current position to the left. The number of decimal places moved must be the same as the exponent. Fill the spaces with zeros. 7.88 x 10 -4 From here …. move decimal point 4 places to the left (you need to write 3 zeros) Answer:.000788

24. Let’s try this problem… Change 9.12 x 10 -3 to standard form 9.12 x 10 -3 Move the decimal point 3 places to the left You will need to write 2 more zeros Answer:.00912 or.009 12

25. Arrange these numbers from the largest to the smallest. 6.5 x 10 4 5.8 x 10 -3 - 3.4 x 10 5 9.2 x 10 -2 7.01 x 10 -1 4.17 x 10 8 2.2 x 10 6

26. Multiplying Numbers in Scientific Notation ( 4.2 x 10 3 ) ( 6.01 x 10 4 ) 1) Multiply the first factors : (4.2 x 6.01) 2) Add the powers of 10: 10 3+4 ANSWER: 25.2 x 10 7

27. Dividing Numbers in Scientific Notation (3.0 x 10 5 ) / (6.0 x 10 2 ) 1)Divide the first factors: 3.0 / 6.0 2 ) Subtract the powers of 10 10 5 – 2 ANSWER: 0.5 x 10 3 = 5.0 x 10 2

28. Adding and Subtracting Numbers in Scientific Notation If you are adding and subtracting numbers in scientific notation without a calculator: first,adjust the numbers so that the exponents are the same ( 5.4 x 10 3 ) + ( 8.0 x 10 2 ) 1) Adjust second number 8.0 x 10 2 = 0.8 x 10 3 2) Add the two numbers (5.4 x 10 3 ) + (0.8 x 10 3 ) ANSWER: 6.2 x 10 3