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APPENDIX 4
Scientific Notation
A4.1 Multiplying and Dividing
Numbers in Scientific Notation
Most scientific calculators will multiply and divide numbers in scientific notation;
however, it is important to understand what is happening. To multiply numbers expressed in scientific notation, multiply the decimal parts of the number and add the
exponents:
(A 10n) (B 10m) (A B) 10nm
To divide numbers in scientific notation, divide the decimal parts and subtract
the exponents:
(A 10n)/(B 10m) (A/B) 10nm
EXAMPLE A4.1
Multiplying Numbers Expressed
in Scientific Notation
(1.5 103) (3.8 105) (1.5 3.8) 1035
5.7 108
3
5
(1.2 10 ) (5.3 10 ) (1.2 5.3) 103(5)
6.4 102
YO U R T U R N
Multiplying Numbers Expressed
in Scientific Notation
(3.1 108) (2.8 104)
Answer: 8.7 1012
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Scientific Notation
EXAMPLE A4.2
Dividing Numbers Expressed
in Scientific Notation
(5.2 103)/(2.8 105) (5.2/2.8) 103(5)
1.9 108
(1.5 103)/(3.8 105) (1.5/3.8) 1035
0.39 102
3.9 103
YO U R T U R N
Dividing Numbers Expressed
in Scientific Notation
(3.1 108)/(2.8 104)
Answer: 1.1 104
A4.2 Adding and Subtracting
Numbers in Scientific Notation
To add or subtract numbers in scientific notation, first express each quantity with
the same exponent, then add or subtract the decimal parts and leave the exponent
unchanged.
(A 10n) (B 10n) (A B) 10n
(A 10n) (B 10n) (A B) 10n
EXAMPLE A4.3
Adding Numbers Expressed in Scientific Notation
(3.0 104) (2.60 105) (3.0 104) (26.0 104)
(3.0 26.0) 104
29.0 104
2.90 105
YO U R T U R N
Subtracting Numbers Expressed
in Scientific Notation
(3.1 107) (2.0 106)
Answer: 2.9 107