Download Number Systems, Exponent Rules and Scien - Math

Name________________________________
Date __________
Mr. Tallman
Math 8R
Review #1 – Number Systems, Exponent Rules and Scientific Notation
Word Bank
Integer
Rational Number
Whole Number
Irrational Number
Use the word bank above to fill in the blank in the following statements.
1) A number that contains a non-terminating, non-repeating decimal is a(n)
______________________________
2) {0, 1, 2, 3, 4…..} is the set of _________________________________.
3) A number that can be written as a fraction and/or a terminating or repeating decimal is
a(n) ________________________________________.
4) The set of positive AND negative whole numbers is the set of ____________________________.
Now, You Try!
Write if each number below is Rational (R) or Irrational (I).
5) √3
6) −
2
7) √225
8) 0. 3̅
5
9) To which of the following does √16 NOT belong?
A) Integers
B) Real Numbers
C) Rational
Numbers
D) Irrational
Numbers
10) Between which two integers does √45 lie between?
A) 5 and 6
B) 6 and 7
C) 7 and 8
D) 8 and 9
Exponent Rules
Name of Rule
Multiplication Rule
Division Rule
Power of a Power Rule
Negative Exponent Rule
Exponent of 1
Exponent of 0
Rule
Keep the base, add the
exponents
Examples
57 ∙ 52 =
Keep the base, subtract the
exponents
76
=
74
Keep the base, multiply the
exponents
(92 )4 =
Turn the exponent into a
fraction, take the reciprocal
of the fraction, and make
the exponent positive
Any number with an
exponent of 1 equals itself
3−5 =
131 =
Any number with an
exponent of 0 equals 1.
170 =
Now, You Try!
Simplify the following expressions using exponent rules. Write your answer in
exponential form.
11) (𝑥 19 )2
14)
67
6
12)
15)
109
13) 8 ∙ 84
105
59 ×5−4
53
16)
52
52
∙ 80
17) What is the value of 40 + 4−2 ? Write your answer in standard form (no exponents).
Scientific Notation
Example 1) Write the number 340,000 in scientific notation.
Steps for writing a whole number in scientific notation:
Steps
Example
1) Put the decimal point after the first nonzero digit starting from the left side of the
number.
2) Drop all of the zeros after the last nonzero digit. This is your first factor.
3) Count how many places the decimal
point moved. This number is your power
of 10. If the original number is a decimal,
your exponent will be negative.
4) Write your number in scientific
notation.
Example 2) What is 3.5 × 10−6 written in standard form?
Steps for writing a number in scientific notation in standard form:
Steps
1) Identify if the exponent is positive or
negative. If the exponent is positive, you
move the decimal point to the right. If the
exponent is negative, you move the
decimal point to the left.
2) Move the decimal point 6 places to the
left.
3) Write your answer in standard form.
Example
Now, You Try!
18) What is 0.000058 written in scientific notation?
A) 5.8 × 10−6
B) 5.8 × 10−5
C) 5.8 × 105
D) 5.8 × 106
19) The length of the Amazon River in South America is 6,400 kilometers. What is this
length written in scientific notation?
A) 6.4 × 102 km
B) 6.4 × 103 km
C) 6.4 × 104 km
D) 6.4 × 105 km
20) What is 6.92 × 10−3 written in standard form?
A) 0.000692
B) 0.00692
C) 0.0692
D) 0.692
21) A virus is viewed under a microscope. Its diameter is 0.0000002 meters. How would
this length be expressed in scientific notation?
22) The area of Australia is approximately 7.7 × 106 square kilometers. What is this area
written in standard form?