Unit 1: Quiz
1.
Name at least three integers greater than one that are both a perfect
square and a perfect cube. Explain your strategy for determining the
numbers.
2.
What is incorrect about the equation below? Explain the mistake and
write the correct the equation.
43 × 43 = 49
3.
Suppose the government had 5 × 109 new social security numbers that
could be assigned, and each state was allocated the same number of new
social security numbers to assign to new citizens. How many new social
security numbers would be allocated to each state? Explain your thinking,
and leave your answer in scientific notation.
4.
The minimum distance from Neptune to Earth is about 1.196 billion
kilometers. What is 1.196 billion written in scientific notation?
Unit 1
Exponents and
Scientific
Notation
Vocabulary and
Review Booklet
Vocabulary
6.
0.000065 is the wave length of yellow light. Can you express the
measurement using scientific notation?
7.
If the speed of light is 3 x 108 meters/second, how many seconds does it
take light to reach the Earth, if the sun is 1.5 x 1011 meters from Earth?
Write the answer in scientific notation.
8.
Through research, scientists found that the body of a 200 lb person
consists of 3.2 x 10-5 lbs of zinc. In the bodies of 1,500 such people, how
much zinc is present?
9.
If we suppose that the volume of Lake Rason is approximately 2.56 x 105
km3 and Lake Rason is 20 times the volume of Lake Rushy, write the
volume of Lake Rushy (approximately).
Base:
Cube (of a number):
Equivalent Fractions:
Expanded Form (of decimal numbers):
Exponent:
Exponential Notation:
Integer:
10. Scientists discovered that the size of the Antarctic Ocean is 20,330,000
Km2. How big is the Arctic Ocean, if the Arctic Ocean is ¾ of the size of the
Antarctic Ocean?
Properties of Exponents
Raising a number to the power of zero: ____________________________________
Operations with Numbers Written in Scientific Notation:
Adding numbers written in scientific notation:
____________________________________________________________________
____________________________________________________________________
Examples:
Subtracting numbers written in scientific notation:
Practice:
1.
2.
3.
50
120
0.90
4.
( )
5.
𝑥0
1 0
2
Raising a number to a negative exponent: __________________________________
Multiplying numbers written in scientific notation:
____________________________________________________________________
____________________________________________________________________
Examples:
Practice:
Dividing numbers written in scientific notation:
−3
1.
2.
3.
5
12−2
0.9−3
4.
( )
5.
𝑥 −5
1 −4
2
Raising a Power to a Power: _____________________________________________
____________________________________________________________________
____________________________________________________________________
Examples:
Practice:
1.
2.
3.
(53 )3
(122 )3
(0.92 )2
4.
(( ) )
5.
(𝑥 6 )5
3
1 3
2
Power of a Quotient: ___________________________________________________
____________________________________________________________________
____________________________________________________________________
Examples:
Practice:
1.
2.
3.
4.
5.
93
81
23
8
64
42
43
23
125
52
Summary:
Scientific Notation:
Product of Powers: ____________________________________________________
Scientific Notation: ____________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
Examples:
Examples:
Practice:
Writing Numbers in Scientific Notation:
1.
2.
3.
4.
5.
0.000089654
12,340,000,000
0.000000007
5.6
56,000
1.
2.
3.
53 × 53
123 ∙ 122
0.92 (0.92 )
4.
( ) ×( )
5.
𝑥5 × 𝑥9
1 2
1 4
2
2
Quotient of Powers: ___________________________________________________
____________________________________________________________________
____________________________________________________________________
Examples:
Writing Numbers in Standard Form:
1.
2.
3.
4.
5.
4.567 × 105
4.567 × 10−5
−9.8543 × 106
−9.8543 × 10−6
6.7 × 1012
Practice:
1.
2.
3.
4.
5.
68 ÷ 65
23 ÷ 28
69
67
9
𝑥 ÷ 𝑥7
𝑦3
𝑦7
Mixed Practice:
Negative Exponent:
1.
The bedroom of our house is 1,200 cubic meters. We know that there are
3.4 x 109 particles of dust per cubic meter. Write how many particles of
dust are present in the bedroom of our house.
Order of Magnitude:
2.
Find out the weight of 6 billion dust particles, if a dust particle has a mass
of 7.53 x 10-10 g.
Power:
Place Value:
3.
Last month, my friend bought a computer. If it can perform 4.66 x 108
calculations per second, what is the performance of the computer in one
minute?
Scientific Notation:
4.
In Australia, the people use approximately 2,240,000,000 pounds of bread
in a year. How can we write this number in scientific notation?
Square (of a number):
Whole Number:
5.
If a satellite travels 62,000,000 miles from Earth, how can we write it in
scientific notation?
Zero (to the power of zero)