Scientific Notation Scientific Notation is a number written as the product of 2 numbers: a coefficient and 10 raised to a power. This is useful for writing very large or very small numbers.

RULES For Scientific Notation 1. Rewrite your number where there is just 1 non-zero digit with a decimal to the right. 2. Then count the number of spaces the decimal was moved and write that as an exponent.

RULES For Scientific Notation 3. If the original number is greater than one, the exponent is positive. 4. If the original number is less than one, the exponent is negative.

Converting to Scientific Notation Example #1: 1. Find Decimal Point. – 36,000 . Move decimal directly behind the first NON-ZERO number. Count the number of spaces decimal moved.

Converting to Scientific Notation 36,000 Example #1 Continued: –Write the number with the new location of decimal. 3.6 –Add x10 to the end of the new number. 3.6 x 10

Converting to Scientific Notation 36,000 Example #1 Continued: –How many spaces did you move the decimal? 4 spaces –This number becomes the exponent. 3.6 x 10 4 –Is the original number greater or less than 1? greater

Converting to Scientific Notation 36,000 Example #1 Continued: –Since 36,000 greater than 1, the exponent will be positive. –Answer: 3.6 x 10 4

Converting to Scientific Notation Example #2: 0.000403 = 0.000403 = 4.03 X 10 -4

Expanding Scientific Notation If the exponent is positive, move the decimal to the right. If the exponent is negative, move the decimal to the left. Examples: – 2.6 x 104 = – 1.08 x 10‒5 =

Practice Write in Correct Scientific Notation • 6,378,000 6.37 x 106 • 0.000000000154 1.54 x 10‒10 • 91.4 x 104 • 0.000008 9.14 x 105 8 x 10‒6 • 4.67 4.67 x 100

Practice Expand to Standard Notation • 4.5 x 105 • 7.38 x 10‒3 • 2.19 x 100 • 4.92 x 108 • 5.3 x 10‒7

Calculator Input Entering Scientific Notation into Calculator Graphing Calculator: Enter coefficient Press 2nd button Press comma key (an E should appear on screen) Enter exponent.

Calculator Input Entering Scientific Notation into Calculator Scientific Calculator: Enter coefficient Press 2nd button Press x–1 (an E should appear on screen) Enter exponent.

Calculator Input Continue –Guidelines: NEVER type in ‘ x10^ ' Use the (-) sign by the decimal place for negative exponents. NOT the subtraction key. Follow Addition/Subtraction and Multiplication/Division Significant Figures Rules to determine how to round answers.

Calculator Practice First, make sure calculator is in SCI mode. –Graphing Calculator: MODE, SCI, Enter, Clear –Scientific Calculator: Push 2nd, DRG, SCI, Enter

Calculator Practice Perform operations in the calculator. Round answer to the correct number of Significant Digits/Decimal Places. 1.35 x 103 + 4.29 x 105 — 5.2 x 10‒16 = Add/Subtract: Count numbers decimal places. Answer = 4.3 x 105 (6.42 x 10‒2) ÷ (9.2 x 10‒5) = Multiply/Divide: Count numbers sig. figs. Answer = 7.0 x 102

Practice http://janus.astro.umd.edu/astro/scinote/