Mr. Simonds’ MTH 65
Key Concepts:
Scientific Notation
Scientific Notation
A non-zero number written in scientific notation has form
a × 10n where 1 ≤ a < 10
and n is an integer.
Examples
250 = 2.5 × 102
0.36 = 3.6 × 10−1
1, 000 = 1 × 103
Converting between standard notation and scientific notation
The basic concept behind this task is that every action requires an equal but opposite action.
Moving the decimal point left one digit corresponds to the power on 10 increasing by 1 .
Example
2,367 = 2,367 × 100 = 236.7 × 101 = 23.67 × 102 = 2.367 × 103
Let’s note that we could have simply counted to determine that we needed to move the
decimal point left 3 digits (for scientific notation) which means the power on 10 needed
to increase from 0 to 3 .
Moving the decimal point right one digit corresponds to the power on 10 decreasing by 1 .
Example
.0056 = .0056 × 100 = 0.056 × 10−1 = 00.56 × 10−2 = 005.6 × 10−3 = 5.6 × 10−3
Let’s note that we could have simply counted to determine that we needed to move the
decimal point right 3 digits (for scientific notation) which means the power on 10 needed
to decrease from 0 to −33 .
Scientific Notation – Section 6.7|1
Mr. Simonds’ MTH 65
Write each number in scientific notation
−0.000000714
42, 000
Write each number in standard notation
−8.6 × 10−9
−3.7 × 1010
Find each product and/or quotient – write the result in scientific notation.
( 2.0 × 10 )( 3.0 × 10 )
−7
12
2| S c i e n t i f i c N o t a t i o n – S e c t i o n 6 . 7
Mr. Simonds’ MTH 65
( 4.0 × 10 )( 3.0 × 10 )
−1
−9
1.2 × 107
2.4 × 10−3
( −90 )( −0.00000008)
( 20, 000, 000, 000, 000, 000 )( −0.00002 )
Scientific Notation – Section 6.7|3
Mr. Simonds’ MTH 65
Group practice problems on exponents and scientific notation
1. Write each number in scientific notation.
a.
5,312,100
b.
0.0003001
2. Write each number in standard notation.
a.
−7.2 × 10−8
b.
5.22 × 109
7.1 × 100
c.
3. Find each product and/or quotient. Write the result in scientific notation.
a.
( −5.0 × 107 )( −3.0 × 10−4 )
c.
−
1.0 ×101
( 4.0 × 10 )(1.0 × 10 )
−9
7
b.
8.0 × 10−9
1.6 × 10−7
d.
( 20, 000, 000 )( 0.0000000000008)
(.0004 )( 200, 000, 000, 000 )
4. Find each value (back to basic exponent questions – the remainder of the questions are not
about scientific notation.)
a.
−6
−2
b.
−3
−1
c.
( −2 )
−4
d.
⎛ 5⎞
e. ⎜ − ⎟
⎝ 2⎠
1
5 −3
−1
f.
2−3
4−2
5. Completely simplify each expression. Make sure that your final expression contains no negative
exponents.
a.
x5 y −7
x y −1
⎛ 6 a −1 b ⎞
e. ⎜ −7 7 ⎟
⎝b c ⎠
b.
3 x −7
f.
−4 x
c.
4−1 x10
y −5
(6 x y )
27 x8 − 33 x5 + 3 x 2
3 x2
4 y −7
3−1 x −5
2 2
−2
g.
2
3x
−1
6. Perform each division.
a.
d.
b.
17 y 6 + 16 y 5 + 4 y
4 y3
4| S c i e n t i f i c N o t a t i o n – S e c t i o n 6 . 7
h.
1
(9
−1
w y −2 z 0 )
5
−1