Scientific Notation

1. Scientific Notation

2. Let’s Investigate! 6.71 x 1,000,000 = 6,710,000 6.71 x 100,000 = 671,000 6.71 x 10,000 = 67,100 6.71 x 1,000 = 6,710 671 6.71 x 100 = 6.71 x 10 = 67.1 1.) What pattern do you notice? 2.) Multiply 6.71 x 109 6,710,000,000

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

4. Scientific Notation A number is expressed in scientific notation when it is in the form a x 10n where a is between 1 and 10 and n is an integer

5. 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 be between 1 and 10? Between the 2 and the 1

6. 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 1023

7. When changing scientific notation to standard notation, the exponenttells you how many places to move the decimal: With a positive exponent, move the decimal to the right: 4.08 x 103 = 4 0 8 Don’t forget to fill in your zeroes!

8. The exponent tells how many spaces to move the decimal: 7.58 x 105 = 7 5 8 In this problem, the exponent is +5, so the decimal moves 5 spaces to the right.

9. Try changing these numbers from Scientific Notation to Standard Notation: • 9.678 x 104 • 7.4521 x 103 • 8.513904567 x 107 • 4.09748 x 109 96780 7452.1 85139045.67 4097480000

10. Standard Notation to Scientific Notation: 1) First, move the decimal after the first whole number: 3 2 5 8 2) Second, add your multiplication sign and your base (10). 3 . 2 5 8 x 10 3) Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10 3 3 2 1

11. Try changing these numbers from Standard Notation to Scientific Notation: • 9872432 • 34582956 • 8376876027 • 5673 9.872432 x 106 3.4582956 x 107 8.376876027 x 109 5.673 x 103

12. Negative Scientific Notation

13. When using Scientific Notation, there are two kinds of exponents: positive and negative Positive Exponent: 2.35 x 108 Negative Exponent: 3.97 x 10 -7

14. Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be 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

15. When changing scientific notation to standard notation, the exponent tells you if you should move the decimal: With a negative exponent, move the decimal to the left: 4.08 x 10-3 = 4 0 8 Don’t forget to fill in your zeroes!

16. An easy way to remember this is: • If an exponent is positive, the number gets larger, so move the decimal to the right. • If an exponent is negative, the number gets smaller, so move the decimal to the left.

17. The exponent also tells how many spaces to move the decimal: 4.08 x 10-3 = 4 0 8 In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

18. When changing from Standard Notation to Scientific Notation: 4) See if the original number is greater than or less than one. • If the number is greater than one, the exponent will bepositive. 348943 = 3.489 x 105 • If the number is less than one, the exponent will be negative. .0000000672 = 6.72 x 10-8