2.2 Scientific Notation and Significant Figures Scientific Notation: In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg x 602000000000000000000000 ??????????????????????????????????? Scientific Notation: A method of representing very large or very small numbers in the form: M x 10n M is a number between 1 and 10 n is an integer 300,000,000 = 3.0 x 108 .000034 = 3.4 x 10-5 Scientific Notation Rules • Only one number should be to the left of the decimal • This is wrong: 34.0 x 10-4 • This is wrong: .56 x 10-4 • This is correct: 7.2 x 10-4 • If the number goes down, the exponent goes up • If the number goes up, the exponent goes down . 2 500 000 000 9 8 7 6 5 4 3 2 1 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point (This is equal to n) Step #4: Re-write in the form M x 10n 2.5 x 9 10 The exponent is the number of places we moved the decimal. 0.0000579 1 2 3 4 5 Step #1: Insert an understood decimal point (Decimal point is given in this problem) Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n 5.79 x -5 10 The exponent is negative because the number we started with was less than 1. Example: The Distance From the Sun to the Earth is 93,000,000 miles Step #1: 93,000,000. Step #2: 93,000,000 = 9.3000000 Write numbers without zeros: 9.3000000 = 9.3 Step 3: Count how many places you moved your decimal and make that your power of ten. (7 places) Step 4: 9.3 X 107 Example The Distance From the Sun to the Earth is 93,000,000 miles 93,000,000 - Decimal or Standard Form 9.3 X 107 - Scientific Notion Practice Problems: 98,500,000 = 9.85 x 10? 9.85 x 107 64,100,000,000 = 6.41 x 10? 6.41 x 1010 279,000,000 = 2.79 x 10? 2.79 x 108 Practice Problems Convert to scientific notation: 5400000 5.4 x 106 .000045 4.5 x 10-5 Scientific Notation to Standard Form Move the decimal to the right - The number to the power of 10. Example: 3.4 x 105 in scientific notation 3.4 = 340000 (Move the decimal right five places) 340,000 in standard form Practice Problems: 6.27 x 106 6,270,000 9.01 x 104 90,100 4.56 x 10-3 .00456 Significant Figures The measurable units of a measuring device plus one estimated digit. Significant Figures .Pacific -----------------------Atlantic Practice Problems • • • • • • 34.007 .0078 234000 6700.100 4000.00 1.005 Pie Graph and Table A pie chart is a circular chart divided into sectors, each sector shows the relative size of each value. Bar Graphs A bar graph is a graph drawn using rectangular bars to show how large each value is. (The bars can be horizontal or vertical) Line Graphs A line graph is a graph that uses points connected by lines to show how something changes in value (as time goes by, or as something else happens).

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