Transcript Standard Form to Scientific Notation

Standard Form to
Scientific Notation
Day 41
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.
Find a number bigger
than 1, less than 10
1. 8.2
a. Only 2 decimal places
b. This is your NEW
decimal
2.
Multiply by 10 ( x 10)
2. 8.2 x 10
3. Count decimal spaces
from NEW to OLD (this
is your exponent on 10)
3. 7 Spaces
(8.2 x 107)
4.
4. Right
LEFT = NEGATIVE
RIGHT = POSITIVE
(exponent)
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.
Example 1:
Write 0.00709 in scientific notation.
0.00709 Move the decimal to get a number between 1
and 10.
7.09  10
(*you want only one number
behind 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
