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Chemistry: The Central Science (11th Edition)

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Unformatted text preview: APPENDIX 1104 Mathematical Operations A.l EXPONENTIAL NOTATION The numbers used in chemistry are often either extremely large or extremely small. Such numbers are conveniently expressed in the form N><10" where N is a number between 1 and 10, and n is the exponent. Some examples of this exponential notation, which is also called scientific notation, follow. 1,200,000 is 1.2 X 106 (read ”one point two times ten to the sixth power”) 0.000604 is 6.04 X 10’4 (read ”six point zero four times ten to the negative fourth power”) A positive exponent, as in the first example, tells us how many times a number must be multiplied by 10 to give the long form of the number: 1.2 x 106 = 1.2 x 10 x 10 x 10 x 10 x 10 x 10 (six tens) : 1,200,000 It is also convenient to think of the positive exponent as the number of places the decimal point must be moved to the left to obtain a number greater than 1 and less than 10: If we begin with 3450 and move the decimal point three places to the left, we end up with 3.45 X 103. In a related fashion, a negative exponent tells us how many times we must divide a number by 10 to give the long form of the number. _4 _ 6.04 _ 6.04 X 10 10 X 10 X 10 X 10 0.000604 It is convenient to think of the negative exponent as the number of places the decimal point must be moved to the right to obtain a number greater than 1 but less than 10: If we begin with 0.0048 and move the decimal point three places to the right, we end up with 4.8 X 10—3. In the system of exponential notation, with each shift of the decimal point one place to the right, the exponent decreases by 1: 4.8 x 10’3 = 48 x 10’4 Similarly, with each shift of the decimal point one place to the left, the exponent increases by 1: 4.8 x 10’ = 0.48 x 10’2 Many scientific calculators have a key labeled EXP or EE, which is used to enter numbers in exponential notation. To enter the number 5.8 X 103 on such a calculator, the key sequence is Imam->- On some calculators the display will show 5.8, then a space, followed by 03, the exponent. On other calculators, a small 10 is shown with an exponent 3. ...
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