| If you need to work with really large
numbers (as in astronomy) or really small numbers (as in biology), you
will find it cumbersome to write the numbers and do basic calculations. |
the speed of light is 4,270,615,200 mph a typical bacterium weighs .000000004 gm |
| Scientific
Notation puts such numbers in a more usable form: |
d.nnnnn x 10p |
| The d.nnnnn is just the first
few digits of the number - one digit between 1 and 9 (inclusive)
followed by as many digits as desired from the number |
the first part of 4,270,615,200
would be 4.27 or maybe 4.2706 |
| If it is important to do
computations to high degrees of accuracy, you would include a lot of
digits. Mostly, 2 or 3 digits after the decimal point are quite
sufficient. |
Pick a point to truncate (cut
off) the original number. Keep all the digits in the right order. Make
sure you round the last digit you keep. |
| The other part of the number
takes care of the fact that your original number may be in the billions
or the billionths but the first part is between 1 and 10. |
4.27 is MUCH smaller than 4,270,615,200 |
| Consider how far you had to move
the decimal point to get d.nnnnn. This becomes the exponent. |
We had to move the decimal point
9 places to the left, so we use 109: 4.27
x 109 |
| If you moved the decimal point
to the left, the exponent is positive. If you moved the decimal point
to the right, the exponent is negative. |
.000000004 becomes 4.00 x 10-9 |
| Remember that the first part
must be a number greater than or equal to 1 and less than 10. There is
ALWAYS exactly one digit to the left of the decimal point. If the
number is negative, its scientific notation also has a minus sign in
front - this does not change. |
Examples: 4.792 x 1016 1.00082 x 10-8 -5.928 x 10-22 |
| Converting from scientific
notation to standard notation is pretty simple: if the exponent is
positive, move the decimal that many places to the right (adding 0s as
necessary). If the exponent is negative, move the decimal that many
places to the left (adding 0s as necessary) |
2.92 x 105 becomes
292,000 -8.65 x 10-6 becomes -.00000865 |
| Arithmetic: addition and
subtraction. You are going to have to change each number in scientific notation into a form with the SAME EXPONENT. Otherwise it will not be possible to add or subtract them. |
3.515 x 104 + 1.602 x
105 change to 3.515 x 104 + 16.02 x 104 now add 19.535 x 104 and change to proper form: 1.9535 x 105 |
| multiplication and division.
This is much more common in science and much easier to do: multiply the
front parts, and add the exponents. Then change to proper form. |
2.82 x 106 • 5.09 x 10-11
= 14.3538 x 10-5 = 1.43538 x 10-4 |
| Note that a negative exponent is
totally independent from a negative number. Don't confuse the two minus
signs. |
