In most situations we use numbers with at most 5 digits, $123.99, 11:30 am, 2300 miles. Identifying numbers such as social security numbers and phone numbers are conveniently divided into groups, (123) 456-7890. A calculator that displays eight digits is more than adequate for all computation involving such numbers.
But there are other topics such as a deficit and the national debt, when we talk about billions,
1000000000,
and trillions,
1000000000000,
of dollars.
In science we sometimes see numbers such as
100000000000000000000,
or
0.00000000000000000001,
which are almost impossible to name.
Scientific notation is an extension of the usual decimal notation which makes handling such numbers easy.
The number 12.34 can be written as
| ... | ... | |
| 123400.E-4 | 123400.x10-4 | |
| 12340.E-3 | 12340.x10-3 | |
| 1234.E-2 | 1234.x10-2 | |
| 123.4E-1 | 123.4x10-1 | |
| 12.34.E0 | 12.34.x100 | |
| 1.234E1 | 1.234x101 | |
| .1234E2 | .1234x102 | |
| .01234E3 | .01234x103 | |
| .001234E4 | .001234x104 | |
| ... | ... |
The first column is preferred by computer programmers and the second one by mathematicians.
An integer after the E indicates that in order to get the usual decimal notation you have to move the decimal point the indicated number of places to the left if the integer is negative, and, to the right when it is positive.
Moving a decimal point to the right corresponds to multiplying the number by 10, and moving it to the left corresponds to dividing the number by 10.
Thus .01234 x103 can be read as '.01234 times 10 to the third power'.
On the TI-83/84.
- To enter a number in scientific notation press,
[.01234][EE][3][ENTER] to get 12.34
- To enter a negative exponent press,
[12][EE][(-)][4][ENTER] getting 0.0012
Try the following keystrokes,
[number of your choice][ENTER]
[*][10][ENTER]
Now when you press [ENTER], whatever is on the display will be multiplied by 10.
Press [ENTER] at least 15 times.
And the following,
[number of your choice] [ENTER]
[÷][10][ENTER]
Now when you press [ENTER], whatever is on the display will be divided by 10.
Press [ENTER] at least 15 times.