Download Math with Scientific Notation Lecture Notes

Regents Chemistry
Scientific Notation PowerPoint
Lectures Notes
Add/Subtract with identical
exponents
• S.N. expressed in the form of M x
10n
• If the numbers have the same
exponent, n, add or subtract the values
of M and keep the same n
For example…
3.0 x 105 m + 5.0 x 105 m
= (3 + 5) x 105 m = 8.0 x 105 m
8.5 x 103 kg + 3.6 x 103 kg =
12.1 x 103 kg
Add/Subtract with different
exponents
If the exponents are not the same, move the
decimal point left or right until they are the
same. Then add or subtract M.
How do we do this???
Dealing with positive exponents
• 3.0 x 105 also equals 300,000
Count the
moves and
see!
300,000
number gets smaller, so
we need more of a positive
exponent to make an equal value
0.30 x 106
number gets larger, so
we need less of a positive
exponent to make an equal value
30.0 x 104
Dealing with negative exponents
• 3.0 x 10-5 also equals 0.00003
Count the
moves and
see!
0.00003
number gets larger, so
we need less of a negative
exponent to make an equal value
We are moving closer
to the decimal point!
0.30 x 10-4
0.00003
number gets smaller, so
we need more of a negative
exponent to make an equal value.
We are moving further from the
decimal point!
30.0 x 10-6
0.00003
Practice Problems
1.5 x 103 = 0.15 x 10?
0.15 x 104
2.0 x 105 = 200 x 10?
200 x 103
3.6 x
10-3
5.5 x
10-5
= 0.36 x
10?
0.36 x 10-2
10?
5500 x 10-8
= 5500 x
Multiplying with S.N.
(2.0 x 102) (3.0 x 103) =
• Multiply the values of M
• Add exponents
• Multiply units
(2.0) (3.0) = 6.0 x 102+3 = 6.0 x 105
Multiplying with S.N.
When products are larger than 9.9999
(5.0 x 103) (6.0 x 104)
= (5.0 x 6.0) = 30 x 103+4 = 30 x 107
3.0 x
108
But is this
proper form?
Dividing with S.N.
6.0 x 105
2.0 x 102
• Divide the values of M
• Subtract exponents
6.0 / 2.0 = 3.0 x 105-2 = 3.0 x 103
Practice: 10.0 x 105
5.0 x 106
Practice Problems
(6.0 x 105) (3.0 x 104) =
(4.0 x 103) (7.0 x 108) =
(1.0 x 102) (2.0 x 10-4) =
6.0 x 108
2.0 x 104
=
3.0 x 104
18.0 x 109
28.0 x 1011
2.0 x 10-2