Compute with scientific notation
This lesson will show you how to compute with scientific notation. You will learn to add, subtract, multiply, and divide with scientific notation.
It is important to understand how to convert numbers to
scientific notation before starting this lesson.
Add and subtract with scientific notation
Example #1:
Add and subtract 2 × 105 + 4 × 103 and -6 × 105 + 2 × 103 + 9 × 104
When adding or subtracting numbers in scientific notation, you can only add or subtract numbers that have the same exponent. Therefore, first step is to put the ones with the same exponent together.
Addition: 2 × 105 + 4 × 103 + -6 × 105 + 2 × 103 + 9 × 104
(2 × 105 + -6 × 105) + (4 × 103 + 2 × 103) + 9 × 104
Add the numbers you see on the left of 105.This is the number before the multiplication sign. Then, put the sum next to 105 and put the multiplication sign between the sum and 105 . Do the same thing for 103
2 + -6 = -4 and 4 + 2 = 6
2 × 105 + 4 × 103 + -6 × 105 + 2 × 103 = -4 × 105 + 6 × 103 + 9 × 104
Subtraction: 2 × 105 + 4 × 103 - ( -6 × 105 + 2 × 103 + 9 × 104 )
2 × 105 + 4 × 103 - -6 × 105 - +2 × 103 - +9 × 104
2 × 105 + 4 × 103 + 6 × 105 - 2 × 103 - 9 × 104
(2 × 105 + 6 × 105) + (4 × 103 - 2 × 103) - 9 × 104
Add the numbers you see on the left of 105 and put the answer next to 105.
Subtract the numbers you see on the left of 103 and put the answer next to 103.
2 + 6= 8 and 4 - 2 = 2
2 × 105 + 4 × 103 - ( -6 × 105 + 2 × 103 + 9 × 104 ) = 8 × 105 + 2 × 103 - 9 × 104
Observation: a × 10n - a × 10n = 0 × 10n = 0
For example, 8 × 107 - 8 × 107 = 0 × 107 = 0
Multiply and divide with scientific notation
Example #2:
Multiply and divide 64000000 and 0.0008
Multiplication: 64000000 × 0.0008
When multiplying or dividing numbers in scientific notation, it is irrelevant to combine numbers that have the same exponent.
Since 64000000 and 0.0008 are not in scientific notation, put them in scientific notation.
64000000 = 6.4 × 107
0.0008 = 8 × 10-4
64000000 × 0.0008 = 6.4 × 107 × 8 × 10-4 = 6.4 × 8 × 107 × 10-4
Multiply 6.4 and 8. Then, multiply 107 and 10-4
6.4 × 8 = 51.2
107 × 10-4 = 107 + -4 = 103
We get 51.2 × 103
Put 51.2 × 103 in scientific notation
51.2 × 103 = 5.12 × 101 × 103 = 5.12 × 104
Division: 64000000 ÷ 0.0008
64000000 ÷ 0.0008 = (6.4 × 107) ÷ (8 × 10-4)
(6.4 × 10
7) ÷ (8 × 10
-4) =
6.4 × 107
/
8 × 10-4
Divide 6.4 and 8. Then, Divide 107 by 10-4
6.4 ÷ 8 = 0.8
107 ÷ 10-4 = 107 - -4 = 1011
We get 0.8 × 1011
Put 0.8 × 1011 in scientific notation
0.8 × 1011 = 8 × 10-1 × 1011 = 8 × 1010