Part 16 of Chapter 1 in Chemistry

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The description of scientific notion was explained and continues in this lesson. "With numbers expressed in exponential form, you can now use your knowledge of exponents in mathematical operations. An important fact to remember is that in multiplication you add the exponents of 10, and in division you subtract the exponents Addition and subtraction can be performed only if the values have the same exponent. Multiplication: Example 1 (2.3 x 10 to the 5th)(5,0 x 10 to the -12)= Solution: Multiplying the first number in each, you get 11.5 and the addition of the exponents gives 10 to the -7. Now changing to a number with only one digit to the left of the decimal point gives you 1.15 x 10 to the -6 for the answer. Example 2 : (5.1 x10 to the -6)(2 x 10 to the -3) = Solution: (5,1 x 10 to the -6)(2 x 10 to the -3)=10,2 x 10 to the -9=1.02 x 10 to the 10 to the -8 Example 3: (3 x 10 to the 5th)(6 x 10 to the 3rd)= 18 x 10 to the 8th= 1.8 x10 to the 9th Division: (Notice that in division the exponents of 10 are subtracted.) Example 1: (1.5 x 10 to the 3rd) / (5.0 x 10 to the -2 = Solution: (1.5 x 1 to the 3rd) / (5.0 x 10 to the -2) = 0.3 x 10 to the 5th = 3 x 10 to the 4 Example 2: (2.1 x 10 to the -2) / (7.0 x 10 to the -3) = Solution:(2.1 x 10 to the -2) / (7.0 x 10 to the -3) = 0.3 x 10 to the 1 = 3 Addition and Subtraction: Example 1: 4.2 x 10 to the 4 kg + 7.9 x 10 to the 3 kg = Solution: 4.2 x 10 to the 4 kg +0.79 x 10 to the 4 kg so that the exponents of 10 are the same = 4.99 x 10 to the 4 kg = 5.0 x 10 to the 4 kg Apply the same process to subtraction problems. DIMENSIONAL ANALSIS 9FACTOR-LABEL METHOD OF CONVERSION 'When you are working problems that involve numbers with units of measurement, itis convenient to use this method so that you do not become confused in the operation of multiplication or division. For example, If you are changing 0.001 kg to milligrams, you set up each conversion as a fraction so that all the units will factor out except the one you want in the answer." Example 1: 1 x 10 to the -3 kg canceled out x 1 x 10 to the 3 g canceled out/ 1 kg canceled out x 1 x 10 to the 3 mg/ 1 g canceled out =1 x 10 to the 3 mg Solution: "the kilogram in the denominator of the first fraction can be factored out with the original kilogram unit. The numerator is equal to the denominator except that is expressed in smaller units."