Transcript Standard Form to Scientific Notation

Standard Form to
Scientific Notation
Learning Target:
Students can convert numbers from standard form into scientific
notation.
What is scientific Notation?
Scientific notation is a way of
expressing really big numbers or really
small numbers.
 It is most often used in “scientific”
calculations where the analysis must be
very precise.

Why use scientific notation?
For very large and very small numbers,
these numbers can be converted into
scientific notation to express them in a
more concise form.
 Numbers expressed in scientific
notation can be used in a computation
with far greater ease.

Let’s compare the two…
STANDARD FORM
SCIENTIFIC
NOTATION


9,200,000,000,000,000
 .0000000000254
 -23,000,000,000
 -.000091
9.2 x 1015
 2.54 x 10-11
 -2.3 x 1010
 -9.1 x 10-5
1. An ordinary quarter contains about
97,700,000,000,000,000,000,000 atoms.
2. The average size of an atom is about 0.00000003
centimeters across.
These very long numbers are written in
**STANDARD FORM**
**The length of these numbers in standard
notation makes them awkward to work with.
Scientific notation is a shorthand way of writing
numbers – instead of standard notation.
Standard Form
Scientific Notation
82,000,000.
1.
Write the number such
that there is one digit to
the left of the decimal.
a.
b.
The number is between 1
and 10.
This is your NEW decimal.
Original decimal
1) 8.2
New decimal
2. Count decimal spaces
2) 8.2000000.
from NEW decimal to the
Moving to the right, so the
original decimal (this is
exponent is positive.
your exponent for 10)
3. MOVE RIGHT = POSITIVE 3) 7 Spaces to the right
MOVE LEFT = NEGATIVE
(8.2 x 107)
(exponent)
Scientific Notation
In scientific notation the number of atoms in
a quarter (97,700,000,000,000,000,000,000 )
is
9.77  1022
and the size of each atom (0.00000003) is
3.0  10–8 centimeters across.
Note that the exponent is
negative since we are moving
decimal to the left.
Example 1:
Write 0.00709 in scientific notation.
0.00709 Move the decimal to get a number between 1
and 10.
7.09 
(*you want only one number to
the left of the decimal)
Set up in scientific notation.
Think: The decimal needs to move left to change 7.09 to
0.00709, so the exponent will be negative.
Think: The decimal needs to move 3 places.
0.00709 written in scientific notation is 7.09  10–3.
Check 7.09  10–3 = 7.09  0.001 = 0.00709
Example 2:
A pencil is 18.7 cm long. If you were to lay 10,000
pencils end-to-end, how many millimeters long
would they be? Write the answer in scientific
notation. Hint:
K
H
D
M
D
C
M
1. Convert from cm to mm
2. Find the length of 10,000
pencils
1 cm = 10 mm
18.7 cm = 187 mm
187 mm  10,000
1,870,000 mm
Multiply by 10
Find the total length.
Multiply
Example 3 continued:
1,870,000 mm
Set up scientific notation.
In scientific notation the 10,000 pencils would be 1.87  106
mm long, laid end-to-end.
Remember…

If the original number was less than 1,
then the exponent is negative. If the
original number was greater than 1,
then the exponent is positive.
Example 4
Given: 289,800,000
 Use: 2.898 (moved 8 places)
 Answer: 2.898 x 108

Example 5
Given: 0.000567
 Use: 5.67 (moved 4 places)
 Answer: 5.67 x 10-4
