1. 4.8 Scientific Notation

2. When working with very large (astronomical!) numbers or very small (microscopic!) numbers, it is easier to write the numbers in scientific notation. Why use scientific notation?? Ex. We can estimate the number of stars in the Milky Way galaxy as roughly 100 billion (100,000,000,000) The diameter of a hydrogen atom is 0.00000000024 m

3. We can estimate the number of stars in the Milky Way galaxy as roughly 100 billion (100,000,000,000) The diameter of a hydrogen atom is 0.00000000024 m It is MUCH easier to write these numbers using scientific notation. There are two parts to scientific notation… 1.The number (which MUST be greater than or equal to 1 and less than 10) 2. The number 10 with an exponent A positive exponent indicates a large number. A negative exponent indicates a small number.

4. To write 100,000,000,000 in scientific notation, “move the decimal point” so that the number part is between 1 and 10, count as you move… We can estimate the number of stars in the Milky Way galaxy as roughly 100 billion (100,000,000,000) 100,000,000,000 11 10 9 8 7 6 5 4 3 2 1 In scientific notation…. 1.0 * 10 11

5. To write 0.00000000024 in scientific notation, “move the decimal point” so that the number part is between 1 and 10, count as you move… The diameter of a hydrogen atom is 0.00000000024 m 0.00000000024 1 2 3 4 5 6 7 8 9 10 In scientific notation…. 2.4 * 10 -10

6. Examples: 3000 3.0 × 10 2 3.0 × 10 3 SCIENTIFIC NOTATIONSTANDARD FORM 300 3250 3.25 × 10 3 32,500,000 3.25 × 10 7 0.03 3.0 × 10 -2 0.0003 3.0 × 10 -4 0.0000000325 3.25 × 10 -8 0.00000000032 3.2 × 10 -10

7. 3000 3.0 × 10 2 3.0 × 10 3 SCIENTIFIC NOTATION STANDARD FORM 300 3250 3.25 × 10 3 32,500,000 3.25 × 10 7 0.03 3.0 × 10 -2 0.0003 3.0 × 10 -4 0.0000000325 3.25 × 10 -8 0.00000000032 3.2 × 10 -10 1.The number (which MUST be greater than or equal to 1 and less than 10) 2. The number 10 with an exponent A positive exponent indicates a large number. A negative exponent indicates a small number. When writing a number in scientific notation there are 2 parts: Number between 1 and 10 10 raised to an exponent

8. EXERCISES: Express in scientific notation. 1. 450 = ___________________ 2. 7500 = ___________________ 3. 12,000,000 = ___________________ 4. 720,000,000,000 = ___________________ 5. 0.00325 = ___________________ 6. 0.000000246 = ___________________ 7. 0.00000000325 = _______________ 8. 0.00000000436 = _________________ 9. 480,000,000 = __________________ 10. 93,200,000,000 = ________________ Now try some:

9. EXERCISES: Express in standard notation. 1) 2 x 10 3 = ___________________ 2) 2.331 x 10 5 = ___________________ 3) 9.51 x 10 12 = ___________________ 4) 5 x 10 -3 = ___________________ 5) 7.6278 x 10 -5 = ___________________ 6) 2.12 x 10 -2 = ___________________ 7) 3.14 x 10 -4 = ___________________ 8) 5.213 x 10 3 = ___________________ 9) 7.49 x 10 4 = ___________________ 10) 9.2 x 10 2 = ___________________ Now try some: