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 × 10
^{5} + 4 × 10
^{3} and 6 × 10
^{5} + 2 × 10
^{3} + 9 × 10
^{4}
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 × 10
^{5} + 4 × 10
^{3} + 6 × 10
^{5} + 2 × 10
^{3} + 9 × 10
^{4}
(2 × 10
^{5} + 6 × 10
^{5}) + (4 × 10
^{3} + 2 × 10
^{3}) + 9 × 10
^{4}
Add the numbers you see on the left of 10
^{5}.This is the number
before the
multiplication sign. Then, put the sum next to 10
^{5} and put the multiplication sign between the sum and 10
^{5} . Do the same thing for 10
^{3}
2 + 6 = 4 and 4 + 2 = 6
2 × 10
^{5} + 4 × 10
^{3} + 6 × 10
^{5} + 2 × 10
^{3} = 4 × 10
^{5} + 6 × 10
^{3} + 9 × 10
^{4}
Subtraction: 2 × 10
^{5} + 4 × 10
^{3}  ( 6 × 10
^{5} + 2 × 10
^{3} + 9 × 10
^{4} )
2 × 10
^{5} + 4 × 10
^{3}  6 × 10
^{5}  +2 × 10
^{3}  +9 × 10
^{4}
2 × 10
^{5} + 4 × 10
^{3} + 6 × 10
^{5}  2 × 10
^{3}  9 × 10
^{4}
(2 × 10
^{5} + 6 × 10
^{5}) + (4 × 10
^{3}  2 × 10
^{3})  9 × 10
^{4}
Add the numbers you see on the left of 10
^{5} and put the answer next to 10
^{5}.
Subtract the numbers you see on the left of 10
^{3} and put the answer next to 10
^{3}.
2 + 6= 8 and 4  2 = 2
2 × 10
^{5} + 4 × 10
^{3}  ( 6 × 10
^{5} + 2 × 10
^{3} + 9 × 10
^{4} ) = 8 × 10
^{5} + 2 × 10
^{3}  9 × 10
^{4}
Observation: a × 10
^{n}  a × 10
^{n} = 0 × 10
^{n} = 0
For example, 8 × 10
^{7}  8 × 10
^{7} = 0 × 10
^{7} = 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 × 10
^{7}
0.0008 = 8 × 10
^{4}
64000000 × 0.0008 = 6.4 × 10
^{7} × 8 × 10
^{4} = 6.4 × 8 × 10
^{7} × 10
^{4}
Multiply 6.4 and 8. Then, multiply 10
^{7} and 10
^{4}
6.4 × 8 = 51.2
10
^{7} × 10
^{4} = 10
^{7 + 4} = 10
^{3}
We get 51.2 × 10
^{3}
Put 51.2 × 10
^{3} in scientific notation
51.2 × 10
^{3} = 5.12 × 10
^{1} × 10
^{3} = 5.12 × 10
^{4}
Division: 64000000 ÷ 0.0008
64000000 ÷ 0.0008 = (6.4 × 10
^{7}) ÷ (8 × 10
^{4})
(6.4 × 10
^{7}) ÷ (8 × 10
^{4}) =
6.4 × 10^{7}
/
8 × 10^{4}
6.4 × 10^{7}
/
8 × 10^{4}



6.4 × 10^{7}
/
8 × 10^{4}



Divide 6.4 and 8. Then, Divide 10
^{7} by 10
^{4}
6.4 ÷ 8 = 0.8
10
^{7} ÷ 10
^{4} = 10
^{7  4} = 10
^{11}
We get 0.8 × 10
^{11}
Put 0.8 × 10
^{11} in scientific notation
0.8 × 10
^{11} = 8 × 10
^{1} × 10
^{11} = 8 × 10
^{10}

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