Page 22 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 1] USEFUL MATH 7

SOLVED PROBLEM 1.14
−5
Examples of addition and subtraction. Note that 10 −2 is larger than 10 −3 and that 10 −4 is larger than 10 .
4
2
4
4
6 × 10 + 5 × 10 = 0.06 × 10 + 5 × 10 = 5.06 × 10 4
2 × 10 −2 + 3 × 10 −3 = 2 × 10 −2 + 0.3 × 10 −2 = 2.3 × 10 −2
7 + 2 × 10 −2 = 7 + 0.02 = 7.02
4
2
4
4
6 × 10 − 4 × 10 = 6 × 10 − 0.04 × 10 = 5.96 × 10 4
3 × 10 −2 − 5 × 10 −3 = 3 × 10 −2 − 0.5 × 10 −2 = 2.5 × 10 −2
7 × 10 −5 − 2 × 10 −4 = 0.7 × 10 −4 − 2 × 10 −4 =−1.3 × 10 −4
−3 −3 −3 −5
6.23 × 10 − 6.28 × 10 =−0.05 × 10 =−5 × 10

SOLVED PROBLEM 1.15
Examples of multiplication and division:
10 4 4−(−3) 4+3 7
5−2
−2
3
5
(10 )(10 ) = 10 = 10 = 10 = 10 = 10
10 −3
−7
5
10 3 3−6 −3 (10 )(10 ) 5−7−2 −4
= 10 = 10 = 10 = 10
10 6 10 2
SOLVED PROBLEM 1.16
A sample calculation:
−5
2
5
2
(460)(0.00003)(100,000) (4.6 × 10 )(3 × 10 )(10 ) 4.6 × 3 10 × 10 −5 × 10 5
= =
−3
3
3
(9000)(0.0062) (9 × 10 )(6.2 × 10 ) 9 × 6.2 10 × 10 −3
2−5+5 2
10 10
= (0.25) = (0.25) = 25
10 3−3 10 0
SOLVED PROBLEM 1.17
Examples of powers of numbers:
2 4
(10 ) = 10 (2)(4) = 10 8
−3 5
(10 ) = 10 (−3)(5) = 10 −15
−4 −3
(10 ) = 10 (−4)(−3) = 10 12
3 2
3 2
2
(3 × 10 ) = 3 × (10 ) = 9 × 10 6
3
−5 3
−5 3
(4 × 10 ) = 4 × (10 ) = 64 × 10 −15 = 6.4 × 10 −14
1 −2 −4 1 8 8 6
−2 −4
(2 × 10 ) = × (10 ) = × 10 = 0.0625 × 10 = 6.25 × 10
2 4 16