SCIENTIFIC
NOTATION
Scientific Notation
• In science, we
typically see very
LARGE or very small
numbers in our
calculations.
• Scientific notation is
used to reduce the
errors when counting
ZEROES.
Scientific Notation
• In order to make this easier,
scientists express numbers in
scientific notation, which uses
powers of 10.
Scientific Notation
• In scientific notation, numbers are
written in the form:
M x 10n
Where the factor M is a number
greater than or equal to 1 but less
than 10 and n is a whole number.
If you have a BIG number…
• You will use POSITIVE powers
• For Example:
100000
• 1 x 1010 = 10000000000
• 1 x 105 =
If you have SMALL numbers…
• You will use NEGATIVE powers
• For
example:
• 1 x 10-5 = 0.00001
• 1 x 10-10 = 0.0000000001
Rules
1. Move the decimals over so that
only one nonzero is to the left of
the decimal.
5,500,000,000
5.500000000
0.0000000067
000000006.7
Rules
2. Count how many spaces you
moved the decimal.
• If you move to the left it’s positive. If
you move to the right it’s negative.
5.500000000
moved 9 spaces left (+9)
000000006.7
moved 9 spaces right (-9)
Rules
3. Get rid of any numbers that are
not significant.
5.500000000
5.5
000000006.7
6.7
Rules
4. Write down the number,
multiplied by 10 to the power of
however many spaces you
found in step 2.
5,500,000,000
5.5 x 109
0.0000000067
6.7 x 10-9
Practice
1. 457800000
2. 260700
3. 2200
4. 0.034
5. 0.000678
6. 0.0000056
4.578x108
5
2.607x10
2.2x103
3.4x10-2
6.78x10-4
5.6x10-6
Scientific Notation -> Standard Form
1. 5.89 x 10-2
2. 4.932 x 10-1
3. 9.7 x 10-6
4. 6.01 x 107
5. 2.485 x 105
6. 1.45 x 103
0.0589
0.4932
0.0000097
60100000
248500
1450