Exponents And Scientific Notation Worksheet
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1
2
3
4An exponential expression is a short form for writing a number where a factor
appears many times.
exponent
base --> 5
3
= 5
X 5 X 5 =
125 power
The exponent 3 tells how many times the base 5 is used as a factor. The exponent
raises the base to a power.
In the same way, the exponential expression x
3
means
x • x
•
x.
Rule
Examples
Any number raised to the first power
is that number.
5' = 5 30,0001 = 30,000
Any number raised to the zero power
is always 1, except that 0° is undefined.
5° = 1 30,000° = 1
For powers of 10, the number of zeros
following the 1 is the same as the
exponent of 10.
10,000,000 = 107 104 = 10,000
For negative powers of integers, the
1
1
1
5 -.3 = _ =
_
expression becomes a fraction with a
numerator of 1 and a denominator of the
positive power.
53
5 X 5 x 5
125
In working with very large or very small numbers, it is often easier to write the
numbers in scientific notation. Scientific notation is the product of two factors: (a
decimal greater than or equal to 1 but less than 10) X (an integer power of 10) or
a
X 10". An example of scientific notation is 8.3 X 104.
Powers of 10
104
10,000
103
1,000
102
100
101
10
10°
.t.
1
10- 1
0.1
10-2
0.01
10-3
0.001
10-4
0.0001
To Write a Standard Number Greater Than 10 in Scientific Notation
• Move the decimal point to make the number a decimal between 1 and 10.
• Count how many places you moved the decimal point to the left.
• Write the number of places the decimal moved as the exponent.
6
You
can use a
scientific calculator
to raise
a number
to a
given
power
using
the y" key.
7 3
7 y x
3 = 343
Exponents and Scientific Notation
35
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