Math 7 SOL Review
Exponent Laws, Negative Exponents,
and Scientific Notation
Name_____________________
Date______________________
I. Exponents are shorthand for repeated multiplication of the same thing by itself.
The exponent of a number says how many times to use the number in
multiplication.
Power
Examples: Numeric Example: 33 = 3●3●3
Variable Example: x4 = x●x●x●x
II. Negative Exponents: A negative exponent just means that the base is on the wrong side of the
fraction line, so you need to flip the base to the other side. The negative exponent does not make the
number negative.
•
•
•
1
102
1
1
1
Write the new fraction simplifying the exponent to a number.
=
=
2
10 10i10 100
Write the negative exponent as a fraction with a positive exponent. 10−2 =
Say the fraction and convert it to a decimal or divide 1 by 100. One-hundredth or
1
= 0.01
100
III. Scientific Notation:
• A number that is written in two parts with multiplication.
• The first number is always between 1 and 10.
• The second number is always a power of 10; or the number 10 raised to an exponent.
Exponent Laws
Use the given numbers to find an equivalent fraction and decimal. Circle all that
Math 7 SOL Review
Exponent Laws, Negative Exponents,
and Scientific Notation
Name_____________________
Date______________________
apply.
1.
2.
10−1
5−1
a) -.10
10−2
a)
1
5
c)
d) .20
1
5
a)
b)
1
100
1
102
b) 0.001
10−3
a) -0.001
5.
10−4
a)
b)
1
104
−
10−5
c) 0.01
e)
e) -0.01
1
100
d)
e)
1
−
1000
1
1000
1
103
c) 0.0001
d) -0.0001
e) -0.004
d)
1
100, 000
f) 0.00001
g) -0.00001
b)
1
10
c).10
b)25
b) 10i10
c)-10
c)0.01
10.
a) 30
b)1000
c) 10i10i10
b)14
d)10
e)
d) 7
1
10
e) 5i5
−
a)10
a) 100
a) 10i10i10i10
1
10
c)
8. 52
9. 102
11.
d)
−
1
104
1
1
1
1
1
a) − i − i − i − i −
10 10 10 10 10
b) ( −10 )( −10 )( −10 )( −10 )( −10 )
a)-10
e)
4
20
1 1 1 1 1
c)
i i i i
10 10 10 10 10
7. 101
d) 10
−
b) -.20
4.
6.
c) .10
1
10
−
3.
b)
c)10,000
1
d) 100
10, 000
d) 10
−
d)
e)-0.01
e)
10i10i10i10
10
e) 40
10i10i10i10i10
10
12.
a) −10i −10i −10i −10i−10
b) ( −10 )( −10 )( −10 )( −10 )( −10 )
c) 10i10i10i10i10
d) 100, 000
f) 50
g) 15
Exponential
Form
Factored Form
Number (in decimal
form)
Words
Math 7 SOL Review
Exponent Laws, Negative Exponents,
and Scientific Notation
10 6
10 5
10 ×10 ×10 ×10 ×10
10 4
10 ?
10 ?
10 ?
10 0
10 −1
10 ×10 ×10 ×10
10 ?
1 1
×
10 10
10
1
10
10 ?
Name_____________________
Date______________________
1,000
100
10
1
.1
One million
One hundred
thousand
Ten Thousand
One thousand
One hundred
Ten
One
One tenth
.01
One hundredth
.001
One thousandth
1,000,000
100,000
10 ?
10 −5
One ten thousandth
1 1 1 1 1
× × × ×
10 10 10 10 10
.00001
One hundred
thousandth
Scientific Notation Practice
Write each number in scientific notation.
1) 0.000000786
2) 3940
3) 4.7
4) 1260000
5) 0.06
6) 175
Write each number in standard notation.
7) 6.17 × 103
8) 7 × 104
9) 7.31 × 106
10) 5.4 × 10−8
11) 6.7 × 10−3
12) 9.59 × 102
Ordering Numbers and Scientific Notation
Scientific Notation
Standard Notation or Decimal Notation
Math 7 SOL Review
Exponent Laws, Negative Exponents,
and Scientific Notation
Name_____________________
Date______________________
Write each list from least to greatest.
13) 2.3 × 10-10, 3 × 10-3, 3 × 10-1, 5.2 × 102, 2.3 × 102, 2.4 × 102 and 2.3 × 104.
-2
-1
2
4
14) 4000, .05, 4 × 10 , 5 × 10 , 40, 4 × 10 , 500, and 5 × 10 .
-4
-2
-2
-2
15) 15. 0, .00052, .0525, 5.23 × 10 , .05, 5.22 × 10 , 5.23 × 10 , 5.24 × 10 , and 5.24.
16)
In the number 324,157.98 what number is in the hundreds place?
17)
In the number 324,157.98 what number is in the hundredths place?
18)
Write a number that has a 4 in the thousands place.
19)
Write a number that has a 4 in the thousandths place.
20)
Write 1,000 as a power of 10.
21)
Write 0.1 as a power of 10.
22)
Write 1 as a power of 10.
23) 5,100 _____ 5.1 × 103
24) 4.3 × 10-4 _____ 4.32 × 10-4
25) 7.8 × 10-7 _____ 7.8 × 10-8
26). 3.2 × 10-10 _____ 3.2 × 10101