Transcript Scientific Notation PowerPoint

Scientific Notation
Write what is in green!
What we know!
• Scientific notation is a short hand way to write
very big or very small numbers
• Scientific Notation has two parts:
• Part A: is a # between 1 and 10 (usually has a decimal
in it)
• Part B: a power of 10
• The two parts are multiplied together
(example: 4.3 x 104 = 43000)


Scientific Notation
Standard Notation
A step by step guide for writing very big
numbers in scientific notation
• Step 1: look at your number
• 450 000
• Step 2: figure out how many times you need to divide
your number by 10 so that the answer will be between 1
and 10 (hint: decimal must move between the first two
digits)
• 450 000 ÷ 10 = 45 000.0
• 45 000.0 ÷ 10 = 4 500.00
• 4 500.00 ÷ 10 = 450.000
• 450.000 ÷ 10 = 45.0000
• 45.0000 ÷ 10 = 4.50000  this number is between 1 and 10
• Step 3: write down your number and count how many
times you divided by 10, that is the number for your
exponent of 10.
• 4.5 x 105
Hint:
• Did you notice the pattern???
•
•
•
•
•
450 000 ÷ 10 = 45 000.0
45 000.0 ÷ 10 = 4 500.00
4 500.00 ÷ 10 = 450.000
450.000 ÷ 10 = 45.0000
45.0000 ÷ 10 = 4.50000
• What happened to the decimal point every time
we divided by 10?
• It moved one place to the left…so could we
simply count the number of times we move the
decimal place to the left to bring the decimal
place to between the first two digits?
So…
•
•
When determining the power of 10 we could
count how many places we need to move the
decimal place to put it between the first two
digits. That number is our power of 10…
Lets try…put the following numbers into
scientific notation:
a)
b)
c)
d)
e)
350 000
57 300
20 460 000
456 000 000
2 400 000
Did you get…
a)
b)
c)
d)
e)
350 000 = 3.5 x 105
57 300 = 5.73 x 104
20 460 000 = 2.046 x 107 or 2.05 x 107
456 000 000 = 4.56 x 108
2 400 000 = 2.40 x 106
Step by step guide for writing a number in
scientific notation back to standard notation
• Step 1: Look at your Number
• 3.6 x 105
• Step 2: expand out your power of 10
• 3.6 x 10 x 10 x 10 x 10 x 10
• Step 3: multiply your answer
•
•
•
•
•
3.6 x 10 = 36
36 x 10 = 360
360 x 10 = 3600
3600 x 10 = 36000
36000 x 10 = 360000
• Step 4: write out your answer
• 3.6 x 105 = 360000
Hint:
• Did you notice a pattern???
•
•
•
•
•
3.6 x 10 = 36
36 x 10 = 360
360 x 10 = 3600
3600 x 10 = 36000
36000 x 10 = 360000
• What happened to the decimal point every time
we multiplied by 10?
• It moved one place to the right…so could we
simply count the number of times we need to
move the decimal place by looking at the
power?
So…lets try these
•
Write the following in standard notation
a)
b)
c)
d)
e)
5.6 x 103
6.78 x 106
7.945 x 102
5.93 x 109
1.7 x 1012
Did you get??
a)
b)
c)
d)
e)
5.6 x 103 = 5600
6.78 x 106 = 6 780 000
7.945 x 102 = 794.5
5.93 x 109 = 5 930 000 000
1.7 x 1012 = 1 700 000 000 000