Exponential Notation
2 × 105
Sliding the decimal point.
Exponential notation lets you move the decimal point in a number.
It simplifies numbers by getting rid of zeros, and making math easier.
Getting rid of zeros helps with big 100,000,000 and small 0.000,000,001 numbers.
1,000,000. can be rewritten as
1. × 106 with the 6 saying the decimal has moved 6 steps left.
0.001 can be rewritten as
1. × 10-3 with the -3 saying the decimal has moved 3 steps right.
1. × 100 is just 1., since 0 means the decimal hasn't been moved.
Three billion, 3,000,000,000. is just 3. × 109. (You can count the steps yourself!.)
Doing math is easier because
you can add to do multiplication,
and subtract to do division.
You see...
10a × 10b = 10 a + b
10a / 10b = 10 a - b
So... Whats a million divided by a thousand?
1,000,000. / 1,000. =
106 / 103 =
106 - 3 =
103 =
1,000.
Also, the zeros can then be used for significant figures.
Here are a few more examples (of little value).
Links
An Exponential Notation Meta Page
See also the links in Scientific Notation .
How to write and speak the exponential notation
Order-of-magnitude calculation - a "you are already doing it" introduction.
ChemTeam: Significant Figures
Chemistry 151: Powers of Ten, Prefixes, Basic Calculator Usage
Details
10a × 10b = 10 a + b
10a / 10b = 10 a - b
(10a)+p = 10 a × p
(10a)-r = 10 a / r
(A × 10a) × (B × 10b) = (A × B) × 10 a + b
(A × 10a) / (B × 10b) = (A / B) × 10 a - b
(A × 10a)+p = A+p × 10 a × p
(A × 10a)-r = A-r × 10 a / r
(A × 10same) + (B × 10same) = (A + B) × 10same
(A × 10same) - (B × 10same) = (A - B) × 10same
(B × 10bigger) + (S × 10smaller) = B × 10bigger
(B × 10bigger) - (S × 10smaller) = B × 10bigger
(S × 10smaller) + (B × 10bigger) = B × 10bigger
(S × 10smaller) - (B × 10bigger) = -B × 10bigger
And if doing "order of magnitude calculation":
10same + 10same ~= 10same
10same - 10same ~= don't do it
10bigger + 10smaller ~= 10bigger
10bigger - 10smaller ~= 10bigger
A __________ function takes the exponential function's output and returns the exponential function's input.
is the relationship linear or exponential
The exponential form of 2x2x2x2x2 is: 25
50 in exponential form is: 5.0 × 101
8², that is the exponential form. :)
36.5 is not an exponential expression! Its value is 36.536.5 is not an exponential expression! Its value is 36.536.5 is not an exponential expression! Its value is 36.536.5 is not an exponential expression! Its value is 36.5
746 in exponential from
Exponential is an adjective.
Exponential relationship!
A __________ function takes the exponential function's output and returns the exponential function's input.
4.75e3 in exponential notation is: 4.75 × 103
is the relationship linear or exponential
The exponential form of 2x2x2x2x2 is: 25
Exponential Technology was created in 1993.
Exponential Technology ended in 1997.
1000000 = 106 in exponential form.
implementation of exponential groth