General Chemistry Principles, Patterns, and Applications, 2011

. (6.923 × 10 −3 ) − (8.756 × 10 −4 )
Solution
a. Both exponents must have the same value, so these numbers are converted to either
(1.36 × 10 2 ) + (47.3 × 10 2 ) or (0.136 × 10 3 ) + (4.73 × 10 3 ). Choosing either alternative gives the same
answer, reported to two decimal places:
(1.36 × 10 2 ) + (47.3 × 10 2 ) = (1.36 + 47.3) × 10 2 = 48.66 × 10 2 = 4.87 × 10 3 (0.136 × 10 3 ) + (4.73 × 10 3 ) =
(0.136 + 4.73) × 10 3 = 4.87 × 10 3
In converting 48.66 × 10 2 to scientific notation, n has become more positive by 1 because the
value of N has decreased.
b. Converting the exponents to the same value gives either (6.923 × 10 −3 ) − (0.8756 × 10 −3 ) or
(69.23 × 10 −4 ) − (8.756 × 10 −4 ). Completing the calculations gives the same answer, expressed to three
decimal places:
(6.923 × 10 −3 ) − (0.8756 × 10 −3 ) = (6.923 − 0.8756) × 10 −3 = 6.047 × 10 −3 (69.23 × 10 −4 ) − (8.756 × 10 −4 ) =
(69.23 − 8.756) × 10 −4 = 60.474 × 10 −4 = 6.047 × 10 −3
Multiplication and Division
When multiplying numbers expressed in scientific notation, we multiply the values of Nand add together
the values of n. Conversely, when dividing, we divide N in the dividend (the number being divided)
by N in the divisor (the number by which we are dividing) and then subtract n in the divisor from n in the
dividend. In contrast to addition and subtraction, the exponents do not have to be the same in
multiplication and division. Examples of problems involving multiplication and division are shown in
Skill Builder ES3.
S K I L L BUILDER ES3
Perform the appropriate operation on each expression and express your answer in scientific notation.
a. (6.022 × 10 23 )(6.42 × 10 −2 )
b. 1.67 × 10 − 24 9.12 × 10 − 28
c. ( 6.63 × 10 − 34 ) ( 6.0 × 10 ) 8.52 × 10 − 2
Solution
a. In multiplication, we add the exponents:
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