Scientific Notation is used in
science to keep track of very large and very small numbers. We
will be describing huge numbers (e.g. light years, moles, mass
of stars/planets, etc.) and tiny numbers (mass of atoms, high
frequency wavelengths, etc.). The steps are easy to go from
standard notation (what you're used to) to scientific notation,
and back again.
If you have a large
number (1,923,847,560) the most important number is the 1
because it means 1 billion. The 9 is the next most important
because it is 9 hundred million; the 2 is 20 million; the 3 is 3
million; the 8 is 8 hundred thousand, and so on.
After realizing how HUGE the 1
billion is, the 560 really doesn't seem that important anymore.
So take the most important number (the 1) and put a decimal
after it to make it a single digit.
1.
The rest of the numbers still
follow.
1.923847560
Now you have reduced 1 billion,
923 million, 847 thousand, 560 to a number less than 2!!! So you
have to count how many times you would have to move the decimal to
get it in the right spot. Each time you move the decimal, you're
multiplying or dividing by 10. So count...
What you have done is moved the
decimal 9 times to the right. In other words, you multiplied by 10
nine times, so you have...
1.923847560 x 109
And in this class I am only going
to have you round to the hundredths place. The rest of the numbers
are so "unimportant" you can get rid of them.
1.92 x 109
Notice, if the 3 (1.923847560
x
109) were a number 5 or more, you would round the 2 up
and you would have
1.93 x 109
Going from Scientific Notation to
Standard is even easier. Take the number 1.92 x 109.
Just move the decimal the number of times of the exponent. So you
would move it 9 times and get...
1920000000 or 1,920,000,000
...and that is extremely close to
what you originally had. If there is a negative exponent, you move
the decimal to the left instead of to the right. We will cover
this in class in more detail and with more examples and I expect
you to know it. This page is just to help you remember or get you
started.
