Scientific Notation: Adding and Subtracting
1. Exponents must be the same or the operation cannot be performed. If the
exponents do not agree, change the decimal and the power of ten notation of
either number so as to agree with the other.
2. Add or subtract the number.
3. Keep the same power of ten.
Examples:
4.2 x 103
= 420 x 101
1
+ 2 x 10
= 2 x 101
(CANNOT DO) 422 x 101 = 4.2 x103
(Use correct scientific notation
and also use the correct number
of significant figures.)
3.3 x 101
= 3.3
x 101
-1
- 7.23 x 10
= 0.0723 x 101
(CANNOT DO)
3.2277 x 101 = 3.2 x 101
Scientific Notation: Multiplying and Dividing
MULTIPLICATION:
1. Multiply the numbers.
2. Add the exponents for the power of ten.
Example: (3.0201 x 102)(2.0 x 101) = 6.0 x 103
(Use correct number of significant figures. Use correct scientific
notation.)
Note: If a power of ten is not expressed, it is understood to be 100, which
equals 1. Thus, 4.0 is understood to be 4.0 x 100.
DIVISION:
1. Divide the numbers as in any division problem.
2. Subtract the denominator power of ten exponent from the numerator power of ten
exponent.
Example:
6.0830 x 104 = 3.52 x 102
1.73 x 102
(Use correct number of significant figures. Use correct scientific
notation).