1.7 Scientific Notation and Significant Figures

Fun with Numbers! Everyone write this down! Mass of the Sun 1,988,500000000000000000000000000 kg Mass of an Electron .000000000000000000000000000000910938291

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 ???????????????????????????????????

M x 10n 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 109 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 10-5 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 93,000,000 - Decimal or Standard Form 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? 64,100,000,000 = 6.41 x 10?

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 9.01 x 104 4.56 x 10-3 .00456 6,270,000 90,100 .00456

Significant Figures The measurable units of a measuring device plus one estimated digit.

Significant Figures .Left -----------------------Right

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).