In science, a unit is a standard amount of
something that we use to make measurements. For example, a
meter is a unit of length and a second is a unit of time. Here are three
units that astronomers use to
measure distances: Astronomical Units ( AU ) , light years ( ly ), and meters (
m ). Since they all measure
distances we can write the two bigger units in terms of meters .
( one hundred fifty billion meters)
( nine quintillion, four hundred sixty
quadrillion meters)
An easier way to write out these huge numbers is to use scientific notation.
Characteristics of scientific notation:
|
 |
exponent |
| coefficient |
|
A number written in scientific notation has
- a coefficient between 1.0 and 9.99999 . . .
- a positive or negative , whole-number exponent |
Remember: Positive exponents mean large numbers.
Negative exponents mean small numbers
How to Convert Numbers To & From Scientific Notation:
Appendix C.2 in the back of your textbook (on page A-6) Gives examples of how to
convert to and from
scientific notation. To learn about or brush up on powers of 10, see section C.1
Exercises: (No calculators, please)
A. Write the following numbers in order , from smallest to largest:
B. Convert the fol lowing distances from scientific to standard notation.
Remember to
write down your units in the answer.
C: Ex press the following distances in scientific
notation, making sure to include the
units:
Scientific Notation AND your Scientific Calculator:
A number like 
just like any other number.
You can multiply it , divide it , etc. If you have already
learned techniques for working with exponents, feel free to use them. If you
haven’t, then you can either
read sections C.1 and C.2 in your book, or just learn how to enter numbers in
scientific notation into your
calculator.
On most scientific calculators, the exponent key is labeled [EE] or
[EXP]. It means “times ten to the
power of”. For example, you can enter 
as 5
[EE] 4 ( or 5 [EXP] 4 ). Similarly, you can enter
as 5 [EE] [+/-] 4 ( or 5
[EXP] [+/-] 4 ) . The [+/-] button is called the integer key.
On some
calculators it is looks like this: [(-)]
As long as the number has fewer digits than your calculator screen. Some
calculators convert small
numbers to standard notation as soon as you hit the [=] key. So
becomes 53 000 and
becomes 0.00053. But very few calculators will convert a number like
to standard notation
because the number just won’t fit on the screen.
Many calculators display just the coefficient and the exponent. But this is
misleading.
Remember to add “ x 10 _” in your head or when you write the number down. A
calculator that is
showing you 
is really
(or 789.0481).
When you actually do a calculation with exponents, treat the whole number
(including exponent) the same
way you would treat any other number. For example try
You should get the number
5. If you don’t, check to see how you are entering the numbers into your
calculator.
D: Multiply or divide as indicated. Put your answer in
scientific notation and let the
units reflect your ope ration (e.g.: 
)
E: For addition or subtraction question below
- first convert all numbers to standard notation
- then perform the operation .
Remember: you can only add or subtract values that share the same unit. We’ll
learn to handle questions with different units at a later time.
