SOL: 7.1
Scientific Notation NOTES
Scientists very often deal with very small and very large numbers, which can lead to a
lot of confusion when counting all those zeros! We have learned to express these small
and large numbers as powers of 10.
A number is expressed in SCIENTIFIC NOTATION when it is written as a product of a
number and a power of ten. The decimal number must be at least one but less than 10.
Converting from Standard Form  to Scientific Notation.
*Place the decimal behind the first digit (non-zero) of the number in standard form.
*Count how many places the decimal moved (left or right).
*The number of jumps/spaces moved is recorded as the EXPONENT in the power of ten.
*If the decimal point is moved to the LEFT it is POSITIVE, and to the right NEGATIVE.
(Is the value getting larger or smaller?)
In Scientific Notation, you are multiplying a decimal by a power of ten.
Example: 3.78 x 104
Type ten to the power of four, or 104, in your calculator – what is its value in standard form?
___________________________
Now multiply this number times the decimal, 3.78. What is 3.78 x 104 in standard form?
_____________________________
What is the difference between the Scientific Notation and Standard Form of the number?
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Converting from Scientific Notation  to Standard Form.
*Locate the exponent. The exponent number tells the number of jumps/spaces to move
the decimal point.
*Move the decimal point LEFT if the exponent is NEGATIVE, and move RIGHT if POSITIVE.
*If the exponent number is NEGATIVE, your number will be less than one.
*If the exponent number is POSITIVE, your number will be greater than one.
(You can always check your answer by converting it back to scientific notation.)
1) 8 x 10-3
2) 9.3 x 105
3) 7.0501 x 109
4) 4.35 x 10-6
Scientific Notation  to Standard form
If the exponent is
_________________
If the exponent is
________________
Decimal x 10
Move the decimal to
the
Move the decimal to
the
LEFT
RIGHT
Write the following numbers in scientific notation form.
1.
4,300
2.
57,000,000
3.
0.00026
4.
0.004
5.
120
6.
0.000001
7.
840,000,000,000
8. 0.0009999
Write the following numbers in standard form.
1) 1.8 x 105
2) 5.04 x 10-5
3) 6.8 x 10-7
4) 2.72 x 109
5) 1.3 x 10
6) 4.08 x 10-1
Put the following in ascending order:
1) 45%, 4.6 x 10-2,
1
,
2
0.045
2) Write 640,000,000 in scientific notation.
A) 6.4 x 107
B) 6.4 x 108
C) 6.4 x 10-7
D) 6.4 x 10-8