Transcript Scientific notation

Today’s lesson . . .
What:
Scientific Notation
Why:
. . . so I can convert between numbers written in scientific notation
and numbers written in standard form; and compare numbers in
scientific notation.
How:
… by taking accurate notes, asking questions, and completing all
practice, including homework.
How do you write a
number in scientific
notation?
How do you compare
numbers written in
scientific notation?
What is it?
We use scientific notation to write very LARGE or very SMALL numbers.
Scientific notation is a number written as a multiplication sentence.
• The leading factor MUST be a number greater than or
equal to 1, but less than 10.
• The second factor must be a power of 10.
Example: 2.5 x 105
How do you write a number in scientific notation ??
There are TWO STEPS:
1) Locate the decimal. If there is no decimal (whole number), place at end of number.
2) Move decimal point until you make a number greater than 1, but less than 10 (the
number of places you move decimal point becomes the exponent number)!
?
2,950,000 = ____________
For example:
Follow the above two steps. Notice that we must move (or “jump”) the decimal point
ACROSS SIX DIGITS in order to make a number greater than 1, but less than 10. Therefore,
“6” is the exponent # . . .
6 is the number of jumps!
Answer: 2.9 x 10 6
1.
5 9 , 0 0 0 , 0 0 0 = 5.9 x 107
7 jumps . . .
First, we will place the decimal at the END of the #!
Then, we will move the decimal point until we create a
number bigger than one, but less than ten . . .
2.
1 4 0 , 0 0 0 , 0 0 0 , 0 0 0 = 1.4 x 1011
11 jumps . . .
3 jumps . . .
3.
9 , 5 0 0 = 9.5 x 103
9 jumps . . .
4.
2 , 5 2 0 , 0 0 0 , 0 0 0 = 2.52 x 109
How do you write a “regular” number from scientific notation ?
There are TWO STEPS:
1) Locate the EXPONENT– this tells you the number of places the decimal will move.
2) Count the existing digits AFTER decimal. How many more do you need to equal
exponent #? This is the number of zeros you add to the end.
?
4.2 x 10 5 = ____________
For example:
Follow the above two steps. Since there is already ONE DIGIT after decimal, we will need
FOUR EXTRA ZEROS at the end. Therefore . . .
Answer: 420,000
We need 7 zeros!
5.
6.32 x 109 = 6,320,000,000
We need 4 zeros!
6.
3.4 x 105 = 340,000
We need 4 zeros!
7.
6 x 104 = 60,000
We need 5 zeros!
8.
2.08 x 107 = 20,800,000
Comparing numbers in scientific notation . . .
9. Order the following from least to great:
2.5 x 10 7
9.4 x 10 4
3.9 x 10 6
3.9
Answer:
9.4 x 10 4
3.9 x 10 6
2.5 x 10 7
Comparing numbers in scientific notation . . .
10. Order the following from greatest to least:
8.5 x 10 4
2.6 x 10 8
1.9 x 10 4
3.9
8.5 x 10 4
1.9 x 10 4
Answer:
2.6 x 10 8
Wrap-it-up (Summary):
END OF LESSON