WorksheetsReal Numbers
Total questions: 145
Worksheet time: 1hrs 13mins
Which set includes all natural numbers and zero?
Integers number set
Whole numbers set
Rational numbers set
Irrational numbers set
Which example is an integer but not a whole number?
Square root of two
Zero counting number
Negative three value
Fraction five ninths
Which number is rational because it can be written as a fraction?
Square root of thirty-one
Square root of six
Square root of five
Three point seven eight
Which statement correctly describes natural numbers?
Start at one and increase
Include irrational roots
Always fractional numbers
Include negative values
Which set contains numbers like 4, −3, and 0?
Natural numbers set
Integers collection
Whole numbers group
Irrational numbers set
Which number belongs to irrational numbers?
Three point seven eight
One and a half decimal
Square root of six
Five sixths fraction
Which choice is a whole number but not a natural number?
Eight over three
Negative eight value
Square root of five
Zero value only
Which description best defines real numbers?
Only nonnegative fractions
Only natural counting set
Only integers and whole
All rational and irrational
Which number is rational and also an integer?
Five over six fraction
Three point seven eight
Square root of five
Zero as a number
Which statement about set relationships is correct?
Natural inside whole
Irrational inside rational
Whole inside natural
Integers inside irrational
Which key concept is emphasized in this lesson’s mathematics focus?
Patterns and change
Quantity and measure
Systems and structures
Relationships
What is the stated global context connecting mathematics to broader ideas?
Orientation in space and time
Scientific and technical innovation
Personal and cultural expression
Fairness and development
Which statement best captures the lesson’s inquiry focus?
Exploring random events without models
Using technology to replace mathematical reasoning
Memorizing formulas for faster calculations
Modeling a systematic relationship in mathematics provides insight into the orientation of space and time
Which learner profile trait is targeted for student development in this lesson?
Communicator
Risk-taker
Inquirer
Balanced
Which example best shows being an inquirer in a math class?
Memorizing all steps without understanding
Copying solutions without questions
Asking how a formula models a real situation
Avoiding mistakes by never trying new problems
Which statement best describes a whole number?
A decimal that never repeats
A negative integer less than zero
A fraction with denominator two
A counting number including zero
Which number is an integer?
√2
−5
3.2
1/4
Which number is rational?
π
0.75
A nonterminating nonrepeating decimal
√3
Which number is irrational?
0.2
7/8
4
π
Which set includes the number 0?
Natural numbers
Counting numbers
Whole numbers
Positive integers
Which description fits natural numbers?
Numbers formed by adding negatives
Counting numbers starting at one
Decimals that do not terminate
Square roots of non-perfect squares
Which statement about real numbers is true?
They include both rational and irrational
They exclude all integers
They are only repeating decimals
They contain only whole numbers
Which of the following is NOT a whole number?
12
0
−3
27
Which example is a terminating decimal, making it rational?
A decimal with no pattern
√5
π
0.5
Which statement correctly classifies −12?
An irrational real number
A natural number only
An integer and rational
A whole number only
Which statement best describes natural numbers?
Fractions between any two integers
Whole numbers including negatives
Counting numbers starting at 1
All numbers on a number line
Which set definition matches whole numbers?
Natural numbers and 0
Integers and their opposites
Decimals that never repeat
Numbers written as ratios
Which list contains only integers?
1, 2, 3, 10
√2, √5, π
−4, −1, 0, 3, 7
1/2, −3, 4, 0.75
Which description fits rational numbers?
Numbers expressible as a fraction
All points on a number line
Counting numbers starting at 1
Numbers with nonrepeating decimals
Which number is irrational?
1/2
0.75
−3
√2
Which statement describes real numbers?
Only counting numbers and zero
All numbers placed on a line
Only ratios of integers
Only nonrepeating decimals
Which example is a whole number but not a natural number?
10
3
1
0
Which number is rational but not an integer?
1/2
−4
7
0
Which property distinguishes irrational numbers from rational numbers?
Decimal never ends or repeats
Can be written as a fraction
Includes negatives and zero
Starts counting at one
Which set includes both whole numbers and their negatives?
Integers
Irrational numbers
Rational numbers
Natural numbers
Which skill is the main learning target shown in the slide image?
Identify and describe sets of real numbers
Solve multi-step algebraic equations quickly
Compute areas of complex three-dimensional solids
Graph linear functions with slope and intercept
Which phrase best completes this statement: By the end of the lesson, I can ______ in the real number system.
prove the Pythagorean Theorem rigorously
memorize every prime number under 100
identify and describe sets of numbers
derive formulas for compound interest
What does the learning target focus on within mathematics?
Calculating large factorial expressions
Solving simultaneous linear systems
Designing geometric transformations
Understanding categories of real numbers
If a lesson aims to identify and describe sets of numbers, which activity best matches that goal?
Estimating surface area of composite solids
Constructing perpendicular bisectors in triangles
Finding the roots of quadratic equations
Classifying numbers as rational or irrational
The phrase 'real number system' most likely refers to which collection?
Complex numbers including imaginary units
Rational and irrational numbers together
Only counting numbers starting at one
Just negative integers and zero
Which student statement shows progress toward the target?
I can recite all triangle congruence theorems
I can draw nets for rectangular prisms
I can explain why √2 is irrational
I can factor every cubic polynomial
A teacher asks: 'Is −5 a rational number?' Which response reflects the learning target?
No, because only whole numbers are rational
Yes, because it can be written as a fraction
No, because negatives are always irrational
Yes, but only when it is a decimal
Which classification would be appropriate when describing 0.333…?
Rational due to repeating decimal pattern
Irrational due to non-terminating decimal
Whole because it is greater than zero
Integer because it is a nonnegative whole
To meet the learning target, which description of √49 is correct?
Irrational because square roots are irrational
Integer because √49 equals seven
Whole because all square roots are whole
Rational because roots cannot be integers
Which example shows identifying and describing sets of numbers?
Saying whole numbers include all negatives too
Claiming fractions are always irrational numbers
Stating natural numbers contain every decimal
Explaining that integers include negatives and zero
Which statement best describes real numbers shown on a number line?
They include only positive whole numbers
They include all rational and irrational values
They are limited to integers from −5 to 5
They exclude decimals and fractions completely
Which of the following is a rational number?
−4.5 written as a fraction
π not repeating or terminating
A non-terminating non-repeating decimal
√21 an irrational square root
Which value is an integer on the diagram?
−1 located at the tick
3/4 between 0 and 1
π placed near three
√21 around four point six
Where is 3/4 located relative to 0 and 1 on the number line?
Between 0 and 1 exactly halfway
Between 0 and 1 closer to 1
Left of 0 near −1
Between 0 and 1 closer to 0
Which pair lists two irrational numbers from the diagram?
π and √21 are both irrational
−1 and −4.5 are irrational
3/4 and √21 are irrational
π and −1 are irrational
Which statement about √21 is correct?
It lies between 4 and 5 on the line
It equals exactly 4 on the line
It equals exactly 5 on the line
It lies between 3 and 4 on the line
Which number has a terminating decimal representation?
A non-repeating infinite decimal
√21 with no finite decimal
π with no finite decimal
−4.5 written as −9/2
Which set classification fits 3/4 best?
Integer and irrational number
Whole number, not rational
Irrational number, not rational
Rational number, not an integer
Which statement about −1 is accurate?
It is an integer and rational
It is irrational and integer
It is whole and irrational
It is natural and irrational
Which choice shows all numbers plotted belonging to the real numbers?
Only −1, 3/4, √21
Only −4.5, −1, 3/4
−4.5, −1, 3/4, π, √21
Only π and √21
Which set is shown as the largest container that includes all other sets in the diagram of number types?
Rational Numbers are the largest container
Whole Numbers are the largest container
Integers are the largest container
Real Numbers are the largest container
Which set contains {1, 2, 3, …} according to the diagram?
Natural Numbers contain {1, 2, 3, …}
Whole Numbers contain {1, 2, 3, …}
Integers contain {1, 2, 3, …}
Rational Numbers contain {1, 2, 3, …}
Where is 0 placed in the nested sets shown?
Included in Whole Numbers set
Only in Integers set
Only in Natural Numbers
Only in Rational Numbers set
Which example from the diagram is irrational?
1.5 is irrational
3.78 is irrational
5/6 is irrational
√2 is irrational
Which statement best describes integers in the diagram?
Integers include negatives, zero, and positives
Integers include only positive counting numbers
Integers include fractions like 6/9 and 8/3
Integers include only zero without negatives
Which of these numbers is shown as rational in the diagram?
√5 is shown as rational
3.78 is shown as rational
-√6 is shown as rational
√31 is shown as rational
Which set is the smallest nested set shown inside the others?
Rational Numbers are the smallest nested set
Natural Numbers are the smallest nested set
Whole Numbers are the smallest nested set
Integers are the smallest nested set
Which placement compares irrational numbers to rational numbers in the diagram?
Irrationals are outside but still real numbers
Irrationals are shown as non-real numbers
Irrationals sit inside the rational region
Irrationals are inside the natural numbers set
Which number would belong to whole numbers based on the diagram examples?
0 belongs to whole numbers
-3 belongs to whole numbers
8/3 belongs to whole numbers
√2 belongs to whole numbers
Which fraction shown is a rational number in the diagram?
-√6 is a rational fraction
6/9 is a rational fraction
√5 is a rational fraction
√31 is a rational fraction
Which set is a subset of Whole Numbers and contains only counting numbers starting at 1?
Integers including negatives and zero
Rational Numbers with fractions
Natural Numbers starting at one
Irrational Numbers with radicals
Which number belongs to the set of Whole Numbers?
√31 nonterminating decimal
8⁄3 greater than two
0 representing no quantity
-8 two units left of zero
Where does the number −3 belong in the real number system?
Whole Numbers including zero
Natural Numbers positive counting
Integers including negatives
Irrational Numbers nonrepeating
Which statement correctly describes Rational Numbers?
Can be written as a⁄b with b≠0
Always positive counting numbers
Never equal to any fraction form
Only square roots of whole numbers
Which example is Irrational according to the diagram?
1.5 terminating decimal
4 whole number example
√5 nonrepeating decimal
6⁄9 simplified fraction
Which set includes all Whole Numbers and their negatives?
Irrational Numbers without ratio
Rational Numbers with fractions
Integers positive and negative
Natural Numbers counting only
Which number listed is rational but not an integer?
0 boundary of whole numbers
5⁄6 proper fraction form
−3 negative whole number
4 exactly a whole number
Which statement about Natural and Whole Numbers is true?
Whole excludes zero completely
Natural contains negatives and zero
Whole is Natural plus the number zero
Natural includes zero by definition
Which number is shown outside the Rational Numbers region?
3.78 finite decimal value
8⁄3 exact fractional value
√31 nonterminating decimal
6⁄9 equivalent to two thirds
Which description best explains why −√2 is not rational?
Its decimal expansion repeats forever
It cannot be expressed as a⁄b
It equals a terminating decimal
It is a negative integer value
Which set includes the numbers 1, 2, 3, and so on without zero?
Whole numbers set
Natural numbers set
Rational numbers set
Integers numbers set
Which number is in the set of whole numbers but not in the set of natural numbers?
Zero, 0
Square root of five
Negative one, −1
One-half, 1/2
Which statement correctly describes integers in the diagram?
Integers exclude whole numbers
Integers include only positives
Integers include zero only
Integers include positives and negatives
Which example is a rational number shown in the diagram?
Square root of five
Square root of two
Negative square root six
Three point seven eight
Which example is an irrational number based on the image?
Square root of thirty-one
Six over nine
One and one-half
Eight over three
Which set contains all other number sets shown in the diagram?
Rational numbers group
Whole numbers group
Real numbers group
Integers group
Where would the fraction 8/3 be placed in the diagram?
Rational numbers layer
Whole numbers layer
Natural numbers layer
Integers numbers layer
Which description best fits rational numbers?
Numbers greater than zero only
Numbers that cannot repeat as decimals
Numbers written as a fraction of integers
Numbers formed only by square roots
Why is 0 placed in whole numbers in the image?
Zero is positive and negative
Zero begins counting sequence
Whole numbers include zero by definition
Natural numbers exclude all even numbers
Which statement about irrational numbers is true here?
They are all negative values
They include non-repeating decimals
Their decimal form repeats evenly
They equal some simple fraction
Which statement best describes an irrational number?
A number whose decimal terminates or repeats eventually
A number written as a over b with b not zero
A number that cannot be written as a over b with integers
A number equal to the square of an integer
Which decimal pattern indicates a rational number?
Square root approximation with different digits each time
Digits change randomly without any repeating block
Terminating after a finite number of digits
Non-terminating and non-repeating digits forever
Real numbers can be classified into which two groups?
Perfect squares and non-squares
Natural and whole numbers only
Rational and irrational numbers
Integers and fractions only
Which property of irrational decimals is correct?
They do not terminate and do not repeat
They end after some digits like 2.75
They equal a ratio of two integers
They have repeating blocks like 0.3333...
Why is √3 considered irrational?
It equals a ratio of two integers
Its decimal repeats as a block
It is the square of an integer
Its decimal neither terminates nor repeats
Which statement about square roots is true?
Square roots are never real numbers
Square root of any integer is rational
Square root of any non-perfect square is irrational
Square root of any perfect square is irrational
Which of the following must be true for a rational number a/b?
a and b are positive and b ≠ 0
a and b are decimals and b ≠ 0
a and b are whole numbers and b = 0
a and b are integers and b ≠ 0
Which decimal suggests an irrational value?
2.1250000000
0.625 with finite digits
3.5 with exact termination
1.4142135623… without repeating block
Which classification fits √5?
Integer, because it equals a whole number
Natural, because it is a counting number
Irrational, because it does not repeat
Rational, because it terminates
Which example is guaranteed rational?
0.7777… repeating sevens forever
√7 with unending changing digits
1.732050808… with no repeating block
Square root of any non-perfect square
Which set includes 0 in the real number system diagram?
Natural numbers set
Whole numbers set
Only integers set
Irrational numbers set
Which number from the list is irrational?
-3 integer
1.21231234… non-terminating
1/2 fraction
0.45 decimal
Where does −8 belong in the classification diagram?
Irrational numbers group
Integers within rational
Whole numbers subgroup
Natural numbers subgroup
Which statement about natural numbers is correct?
They are only irrational
They include all decimals
They start at 1 and increase
They include negative values
Which of these is a rational number shown in the diagram?
π symbol
0.4 repeating
√3 radical
1.21231234…
What is the best classification for 18%?
Rational number type
Whole number type
Irrational number type
Natural number type
Which number belongs to the whole numbers but not the natural numbers?
0 zero
10 positive
9 positive
4 positive
Which is true about integers in the diagram?
Integers are the same as natural
Integers exclude negative values
Integers are a subset of rational
All integers are irrational
Which representation is shown as a rational number example?
√3 radical
−3/4 fraction
π symbol
Nonrepeating decimal
Which choice correctly compares rational and irrational numbers?
Irrational are all whole numbers
Only irrational can be fractions
Both can be written as a/b form
Rational must be negative values
Which statement correctly explains why −25 is rational?
It has a nonrepeating decimal part
It is not an integer value
It can be written as −25 over 1
It cannot be expressed as a ratio
A rational number is defined as a number that can be written as which form?
a plus b with both nonzero
a minus b with a not zero
a times b with b not zero
a over b with b not zero
When −25 is written as −25/1, what are a and b in the form a/b?
a = −25, b = 1
a = 1, b = −25
a = −1, b = 25
a = 25, b = −1
Which condition must be true for a number a/b to be rational?
a and b are fractions, a ≠ 0
a is real, b is irrational
a and b are positive numbers
a and b are integers, b ≠ 0
Choose the correct classification for −25.
Nonreal irrational number
Rational integer number
Irrational whole number
Irrational integer number
Which of the following is NOT a reason that −25 is rational?
Its numerator and denominator are integers
Its denominator can be zero
It equals −25 divided by 1
It can be expressed as a ratio
What does b ≠ 0 ensure in the fraction a/b?
The division is defined
The decimal is repeating
The numerator is positive
The number is irrational
Which form shows −25 as a ratio of two integers?
0/−25
1/−25
−25/0
−25/1
If a number can be written as a/b with a and b integers and b ≠ 0, then the number is
Rational
Irrational
Undefined
Imaginary
Which statement about −25 is true?
It is an integer and rational
It is irrational and noninteger
It cannot be written as a/b
It has a nonterminating decimal
Which statement best describes a rational number?
A number with endlessly random decimal digits
A number expressible as a fraction of integers
A number found only on complex planes
A number that cannot be placed on a number line
Which of the following is irrational?
Negative five divided by one
Three-fourths written as 0.75
The square root of 2 exactly
Twenty over four simplified to five
Which decimal represents a rational number?
0.333… repeating forever
The square root of three
A decimal with no repeat or end
Pi rounded to ten digits
Which number is NOT rational?
Square root of seven
Minus eight over two
Zero point five as one-half
One hundred divided by ten
Which description fits all irrational numbers?
Non-terminating and non-repeating decimals
Terminating decimals with finite digits
Whole numbers and their opposites
Fractions with integer numerators and denominators
Which set contains only rational numbers?
-3, 0, 1/2, 4.25
√5, 2, 7/3, 0
π, √9, 1.2, -1
√2, -4, 0.1, 5
Which statement about π (pi) is true?
It is negative for all circle ratios
It is a whole and natural number
It equals exactly twenty-two over seven
Its decimal never repeats or terminates
Which option shows a rational approximation of √2?
A symbol that cannot be approximated
A non-repeating never-ending decimal
1.41 rounded to two decimals
An exact infinite decimal expansion
Which number is both an integer and rational?
-6 written as -6/1
π expressed as 3.14
√3 expressed approximately
√16 written exactly
Which explanation shows why 0.75 is rational?
It equals three over four exactly
It has digits that never repeat
It is defined by circle circumference
It cannot be written as any fraction
Which statement best describes a rational number?
Equals the square root of any prime
Has digits that never repeat ever
Can be written as a fraction a/b
Is always a positive whole number
Which number is irrational?
-6 as an integer value
4.25 written as 17/4
0 expressed as 0/1
3.14159... with no pattern
Which set includes all negative whole numbers and positive whole numbers and zero?
Natural numbers include negatives
Whole numbers include negatives
Irrational numbers include negatives
Integers include negatives and zero
Which set contains 0 but not -1?
Irrational numbers contain only fractions
Natural numbers include negative one
Integers exclude zero completely
Whole numbers contain zero only
Which choice lists sets from largest to smallest by inclusion?
Integer → Whole → Real
Rational → Real → Natural
Natural → Whole → Irrational
Real → Rational → Integer
Which description fits natural numbers?
Numbers with nonrepeating decimals
Counting numbers starting at 1
All fractions including negatives
Zero and all negative integers
Which number belongs to both rational and integer sets?
0.101001... has patterns
√2 cannot be a fraction
-3 equals -3/1 exactly
π has nonterminating digits
Which statement about real numbers is true?
They include rational and irrational
They exclude all fractional values
They are only whole counting numbers
They are only negative integers
Which number is whole but not natural?
2 is whole and irrational
1 is whole and not natural
-1 is whole and natural
0 is whole but not natural
Which classification is correct for 7.5?
Integer and irrational
Rational but not integer
Irrational and integer
Whole and natural
Which set best describes numbers that can be written as a fraction of integers, like 7/3 or −2?
Natural numbers only
Irrational numbers only
Rational numbers only
Whole numbers only
Which statement about irrational numbers is true?
They are always negative integers
They have terminating decimals
They have repeating decimals
They cannot be written as a/b
Which set includes zero and all positive counting numbers?
Whole number set
Integer set
Natural number set
Irrational number set
Which example is an integer?
√2
3.5
−4
0.25
Which number belongs to the natural numbers?
−1
0
−3
5
Which description matches the integer set?
Positive and negative whole numbers
Only positive counting numbers
All fractions and decimals
Numbers with nonrepeating decimals
Which statement correctly compares whole and natural numbers?
Both exclude zero; both include negatives
Both include fractions; both exclude integers
Whole includes zero; natural excludes zero
Whole excludes zero; natural includes zero
Which number is rational?
√2
π
0.75
√3
Which number set contains all rational and all irrational numbers?
Whole numbers
Real numbers
Integers
Natural numbers
If a number is an integer, which other set must it also belong to?
Rational numbers
Prime numbers
Irrational numbers
Natural numbers
