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Scientific Notation 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. This is essentially a way of writing numbers with large amounts of digits in a condensed form. B. Only significant figures are written when using Scientific Notation. C. It is also based on the powers of 10; but as exponents. • Exponents are whole numbers written in superscript to represent a specific number of places the decimal point has moved. Scientific Notation: • Exponents are whole numbers written in superscript to represent a specific number of places the decimal point has moved. • If the exponent is a positive whole number, the decimal point has been moved to the left. • This would be a larger than 1 number. • If the exponent is a negative whole number, the decimal point has been moved to the right. • This would be a smaller than 1 number. Scientific Notation: D. Numbers written in scientific notation have a basic format: M.N X 10Z • M = First Significant digit in the number (always followed by the decimal point) • N = Second Significant digit in the number, there could be more than 2 sig figs • Z = a whole number representing the number of places the decimal point has moved. For example: 1,000,000.0 g = 1.0 X 106 g 250.0 L = 2.5 X 102 0.000465 m = 4.65 X 10-4 m . 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 Step #4: Re-write in the form M.N x 10z 2.5 x 9 10 The exponent is the number of places we moved the decimal. 0.0000579 1 2 3 4 5 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.N x 10z 5.79 x -5 10 The exponent is negative because the number we started with was less than 1. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION E. ADDITION AND SUBTRACTION 4 x 106 6 + 3 x 10 7 x 106 IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 106 6 10 4 x - 3 x 1 x 106 The same holds true for subtraction in scientific notation. 106 4 x + 3 x 105 If the exponents are NOT the same, we must move a decimal to make them the same. 6 10 4.00 x 4.00 x 6 5 + .30 x 10 + 3.00 x 10 6 4.30 x 10 Move the decimal on the smaller number! 6 10 A Problem for you… -6 10 2.37 x -4 + 3.48 x 10 Solution… -6 002.37 2.37 x 10 -4 + 3.48 x 10 Solution… -4 0.0237 x 10 -4 + 3.48 x 10 -4 3.5037 x 10 PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION MULTIPLICATION AND DIVISION F. MULTIPLICATION Multiplication using Scientific Notation: 1.The significant digits, of each number, are multiplied first. 2.Then the exponents are added together. For example: (2.4 X 105) • (3.6 X 103) = 8.64 X 108 G. DIVISION Division using Scientific Notation: 1.The significant digits are divided first. 2.Then the exponents are subtracted. For example: 2.45 X 1023 = 0.43 X 1011 5.65 X 1012 = 4.3 X 1010