Real Numbers
Subsets
Perfect or Imperfect?
Scientific Notation
Mixed Problems
100
This category contains numbers that are not:
negative, fractions, decimals or the number 0.
Natural Numbers (Counting Numbers)
100
True or False? Irrational numbers are a subset of Rational Numbers.
False
100
√225 = ?
25
100
How is 4,400 written in Scientific Notation?
4.4 x 103
100
How are squares and square roots related?
They are opposites. (inverse relationship) A square is multiplying by itself. A square root is a number that, when multiplied by itself, gives the original number.
200
The number can either be irrational or rational
a REAL number
200
Since Counting Numbers are a subset of Whole Numbers, Whole Numbers are also a subset of Counting Numbers. True or False?
False
200
What two perfect squares does √119 fall between?
√100 and √121
200
0.000005607 converted to Scientific Notation would have a positive exponent.
True or False? Explain why.
False. This is a small number, less than 1. Numbers less than 1 have a negative exponent in Scientific Notation.
200
Estimate the value of √17 and place on a number line.
√17 ≈ 4.1
Teacher will check number lines.
300
-4.5 belongs in which categories?
Rational and Real
300
What is wrong with this statement:
Whole Numbers are a subset of Integers which are a subset of Rational. So all three Categories share each other's numbers.
All three Categories do NOT share each other's numbers. Integers do not contain rational numbers and Whole numbers do not contain integers/rational numbers.
300
Imperfect Squares are: Rational or Irrational
Irrational
300
Which option is written INCORRECTLY in Scientific Notation and WHY?
A - 5.6 x 105
B - 7 x 10-11
C - 0.99 x 103
D - 1.004 x 10-8
Option C is INCORRECT because the number before the decimal is less than 1.
300
How do you convert a number in standard notation to scientific notation?
1. Move the decimal after the first non-zero single digit to create a number between 1 and 9.
2. Count the number of times you moved the decimal.
3. Write the new decimal times 10 to the power of the number of times you moved the decimal.
(Positive exponent if the original value was greater than one. Negative exponent if the original value was less than one.)
400
The decimal 5.6939538 is _______ because it ______
Rational; Terminates (ends)
400
This category contains whole numbers and their opposites and are a subset of rational numbers.
Integers
400
Estimate the value of √79
√79 ≈ 8.8 (8.7 and 8.9 are also acceptable)
400
Which number is larger and WHY?
5.4 x 1032 or 9.3 x 10-43
5.4 x 1032 because the exponent is positive. Moving the decimal to the right would make a larger number.
9.3 x 10-43 has a negative exponent. Moving the decimal to the left would make a much smaller number.
400
The area of a square wall is 182 square feet. Which measurement is closest to the side length in feet of this wall?
13.5 square ft
√182 ≈ 13.5 (approximation, close to 13.5 is acceptable.
500
Name all of the categories that 178 belongs to.
Counting/Natural, Whole, Integer, Rational, Real
500
Which is the correct answer and WHY?
D - Every decimal number is an irrational number is NOT true.
Some decimals are rational. They terminate and are predictable.
500
What is the difference between perfect and imperfect squares?
Perfect Squares have an answer that is a whole number. They're also rational.
Imperfect Squares have an answer that is a decimal. They're also irrational.
500
Order these numbers from least to greatest.
4.8 x 10-4
6 x 102
-10
-10
4.8 x 10-4
6 x 102
500
Paula completely covered a square wall using 87.5 square feet of wallpaper without any overlap. What is the approximate side length of this wall?
√87.5 ≈ 9.3 (approximation, close answers acceptable)