|
|
|
|
|
|
We can now give the rules for converting numbers between scientific notation and
regular numbers...
To convert to scientific notation, from a normal number:
1. move the decimal as many places as needed so that the number is between 1 and
10 (not including 10)
2. multiply that number by ten to the power of however many places you moved the
decimal, and make the power...
 |
|
 |
...negative if you
moved to the right.
Meaning you have
a small number. |
|
|
...positive if you
moved to the left
Meaning you have
a big number. |
|
Example 1: Change 3,960,000 into scientific notation
Here's all the ways to write 3,960,000 as a number times a power of 10 up to a power
of 6. Only the last one is in scientific notation.
3,960,000 = 3,960,000 x 100 -> decimal moved 0 times to left
3,960,000 = 396,000 x 101 -> decimal moved 1 time to left
3,960,000 = 39,600 x 102 -> decimal moved 2 times to left
3,960,000 = 3960 x 103 -> decimal moved 3 times to left
3,960,000 = 396 x 104 -> decimal moved 4 times to left
3,960,000 = 39.6 x 105 -> decimal moved 5 times to left
3,960,000 = 3.96 x 106 -> decimal moved 6 times to left
This one is scientific notation because 3.96 is between 1 and 10.
Example 2: Change .00072 into scientific notation.
Here's all the ways to write .00072 as a number times a power of 10 down to a power
of -4. Only the last one is scientific notation.
.00072 = .00072 x 100 -> decimal moved 0 times to right
.00072 = .0072 x 10-1 -> decimal moved 1 time to right
.00072 = .072 x 10-2 -> decimal moved 2 times to right
.00072 = .72 x 10-3 -> decimal moved 3 times to right
.00072 = 7.2 x 10-4 -> decimal moved 4 times to right
This one is scientific notation because 7.2 is between 1 and 10.
|
|
|