1. Standard Form to Scientific Notation
Day 41
Learning Target:
Students can convert numbers from standard form into scientific notation.

2. 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.

3. 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.

4. Let’s compare the two… SCIENTIFIC NOTATION STANDARD FORM
9,200,000,000,000,000
-23,000,000,000
9.2 x 1015
2.54 x 10-11
-2.3 x 1010
-9.1 x 10-5

5. An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms.
The average size of an atom is about 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.
What is in the pink boxes is what goes in any of the blanks on the Know-It Notes
Scientific notation is a shorthand way of writing numbers – instead of standard notation.

6. Standard Form Scientific Notation 82,000,000
Find a number bigger than 1, less than 10
Only 2 decimal places
This is your NEW decimal
Multiply by 10 ( x 10)
3. Count decimal spaces from NEW to OLD (this is your exponent on 10)
4. LEFT = NEGATIVE
RIGHT = POSITIVE
(exponent)
x 10
3. 7 Spaces
(8.2 x 107)
4. Right

7. 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 ( ) is
3.0  10–8 centimeters across.

8. Write 0.00709 in scientific notation.
Example 1:
Write in scientific notation.
Move the decimal to get a number between 1 and 10.
(*you want only one number behind the decimal)
7.09  10
Set up in scientific notation.
Think: The decimal needs to move left to change 7.09 to , so the exponent will be negative.
Think: The decimal needs to move places
written in scientific notation is  10–3.
Check  10–3 = 7.09  =

9. K H D M D C M Example 2: 1 cm = 10 mm 18.7 cm = 187 mm Multiply by 10
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:
Convert from cm to mm
Find the length of 10,000 pencils
K H D M D C M
1 cm = mm
18.7 cm = mm
Multiply by 10
Find the total length.
187 mm  10,000
Multiply
1,870,000 mm

10. Set up scientific notation.
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.

11. 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.

12. Example 4 Given: 289,800,000 Use: 2.898 (moved 8 places)
Answer: x 108

13. Example 5 Given: 0.000567 Use: 5.67 (moved 4 places)
Answer: 5.67 x 10-4