4.8 Scientific Notation

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 m

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 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.

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, In scientific notation…. 1.0 * 10 11

To write 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 m In scientific notation…. 2.4 *

Examples: × × 10 3 SCIENTIFIC NOTATIONSTANDARD FORM × ,500, × × × × ×

× × 10 3 SCIENTIFIC NOTATION STANDARD FORM × ,500, × × × × × 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 raised to an exponent

EXERCISES: Express in scientific notation = ___________________ = ___________________ 3. 12,000,000 = ___________________ ,000,000,000 = ___________________ = ___________________ = ___________________ = _______________ = _________________ ,000,000 = __________________ ,200,000,000 = ________________ Now try some:

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