Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Rational & Irrational Numbers Practice Quiz

Sharpen math skills with operations and expressions

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art representing a trivia quiz on rational and irrational numbers for high school students.

Which of the following numbers is a rational number?
e
√2
3/4
π
A rational number can be expressed as a fraction of two integers. 3/4 fits that definition.
Which of the following numbers is irrational?
√2
3.25
1/2
4/5
√2 is irrational because it cannot be written as a fraction of two integers. The other options can be expressed as fractions and are therefore rational.
What is a typical characteristic of the decimal representation of a rational number?
It terminates after a few digits only.
It is non-terminating and non-repeating.
It always forms a random sequence.
It either terminates or eventually repeats.
Rational numbers have decimal expansions that either terminate or eventually repeat a pattern. This distinguishes them from irrational numbers which are non-terminating and non-repeating.
Which of these numbers can be written as a ratio of two integers?
√3
5
√7
π
Every integer, including 5, can be written as a fraction (for example, 5/1). This makes it a rational number.
True or False: All integers are rational numbers.
False
Sometimes True
Not enough information
True
Every integer can be expressed as a fraction with denominator 1, which qualifies it as a rational number.
Express the repeating decimal 0.636363... as a fraction in simplest form.
6/11
7/12
7/11
9/11
0.636363... can be written as 63/99, which simplifies to 7/11 after dividing the numerator and denominator by 9.
Which property must a number have in order to be classified as rational?
It has a non-terminating, non-repeating decimal expansion.
It has a terminating or repeating decimal expansion.
It cannot be expressed as a fraction.
It is defined by irrationality.
A rational number is one that can be expressed as a fraction and its decimal will either terminate or eventually repeat a cycle.
What is the sum of a rational number and an irrational number?
Rational
Sometimes rational
Irrational
Depends on the numbers
The sum of a rational and an irrational number is always irrational because the non-repeating decimal part of the irrational number is preserved.
Which of the following operations always produces a rational result when applied to two rational numbers?
Exponentiation
Sine function evaluation
Square Root extraction
Addition
When you add two rational numbers, the result is always rational. The other operations listed do not guarantee a rational outcome.
If x = 2/3 and y = 4, what is x + y expressed as a fraction?
4/3
16/3
10/3
14/3
By converting 4 to 12/3, you add 2/3 + 12/3 to obtain 14/3 in its simplest form.
Which of the following decimals is an example of an irrational number?
0.101001000100001...
0.272727...
0.3333...
0.5
The decimal 0.101001000100001... does not repeat or terminate, a key characteristic of irrational numbers. The other options represent either repeating or terminating decimals.
Express the decimal 0.75 as a fraction in simplest form.
3/4
75/100
7/10
1/2
0.75 is equivalent to 75/100, which simplifies to 3/4 by dividing both numerator and denominator by 25.
Which of the following numbers is not rational?
2
0.875
√5
1/7
√5 cannot be expressed as a fraction of two integers, making it irrational. The other options have clear rational representations.
What is the reciprocal of a rational number expressed as a/b (where a and b are nonzero), and is it rational?
The reciprocal is a/b and it is irrational.
The reciprocal is b^2/a and it is irrational.
The reciprocal is b/a and it is rational.
The reciprocal is 1/(a*b) and it is rational.
The reciprocal of a fraction a/b is b/a. Since both b and a are integers, the result is also a rational number, provided a and b are nonzero.
Which of the following is an example of a repeating decimal that represents a rational number?
0.142857142857...
0.1010010001...
π
0.123456789
0.142857142857... is the repeating decimal form of 1/7, a rational number. The other options either do not repeat regularly or are irrational.
Which statement correctly describes the product of a nonzero rational number and an irrational number?
It can be rational if the irrational number is carefully chosen.
It is undefined.
It is always rational.
It is always irrational.
Multiplying a nonzero rational number by an irrational number preserves the non-repeating, non-terminating nature of the irrational number, resulting in an irrational product.
Why is the number 0.101001000100001... considered irrational?
Because it can be exactly written as a fraction.
Because it repeats a simple pattern.
Because its decimal expansion neither terminates nor repeats.
Because it terminates after a few digits.
The number 0.101001000100001... is irrational because its decimal expansion does not settle into a repeating cycle and does not terminate, which is the hallmark of irrationality.
Which pair of irrational numbers has a sum that is rational?
e and π
π and √2
√2 and -√2
√3 and √5
The sum of √2 and -√2 is 0, which is a rational number. The other pairs do not cancel out to produce a rational sum.
What is the nature of the decimal expansion of the rational number 2/7?
It is non-terminating and non-repeating.
It terminates after two decimal places.
It repeats every 6 digits.
It repeats every 3 digits.
The fraction 2/7 converts to a repeating decimal with a 6-digit cycle, which is a typical property of fractions whose denominators do not factor into 10.
What is the sum of the repeating decimal 0.454545... and the terminating decimal 0.1, expressed as a fraction?
61/100
61/110
71/110
51/110
0.454545... is equivalent to 5/11 and 0.1 is 1/10. Adding these fractions gives (50/110 + 11/110) = 61/110, which is the simplified result.
0
{"name":"Which of the following numbers is a rational number?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"Which of the following numbers is a rational number?, Which of the following numbers is irrational?, What is a typical characteristic of the decimal representation of a rational number?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Understand the definitions of rational and irrational numbers.
  2. Identify examples of rational and irrational numbers from various representations.
  3. Distinguish between rational and irrational numbers using their unique properties.
  4. Apply conversion techniques to express repeating decimals as fractions.
  5. Analyze and solve problems involving the classification of numbers as rational or irrational.

Rational & Irrational Numbers Cheat Sheet

  1. Understand Rational Numbers - Rational numbers are fractions made from two integers, like 3/4 or -5/2, and their decimals always terminate or repeat. Getting comfy with them helps you breeze through basic algebra and real‑world measurements. Check out practice problems
    2. Rational and Irrational Numbers Worksheet, Difference, and Examples
  2. Recognize Irrational Numbers - Irrational numbers can't be written as simple fractions because their decimals neither terminate nor repeat, for example π or √2. Spotting them trains your number‑sense and deepens your understanding of infinite decimals. Explore irrational traits
    3. Rational and Irrational Numbers Worksheet, Difference, and Examples
  3. Classify Numbers Correctly - Every integer is rational (just write it over 1), but only decimals that stop or loop back are rational too. Learning the rules stops you from accidentally calling a never‑ending decimal rational. Dive into the full guide
    4. Study Guide - Identifying Rational and Irrational Numbers
  4. Approximate Irrational Numbers - Since you can't pin down an irrational with a fraction, you use close decimals like 3.14 for π or 1.41 for √2. These handy estimates power real‑life calculations from engineering to cooking. See more examples
    5. Rational and Irrational Numbers Worksheet, Difference, and Examples
  5. Compare and Order Numbers - To rank rationals and irrationals, turn them into decimals, then line them up from smallest to largest. This skill makes solving inequalities and checking work a piece of cake. Practice ordering now
    6. Ordering Rational and Irrational Numbers Worksheet
  6. Identify Common Irrational Numbers - Memorize famous irrationals like π, e, √2, and √3 so they pop out in problems and proofs. Recognizing these constants unlocks shortcuts in geometry, calculus, and beyond. Meet the usual suspects
    7. Rational and Irrational Numbers Worksheet, Difference, and Examples
  7. Practice Converting Decimals to Fractions - Turn repeating decimals into neat fractions (e.g., 0.666… = 2/3) to reinforce why they're rational. This trick is a calculator‑free power move on exams. Master the conversion
    8. Study Guide - Identifying Rational and Irrational Numbers
  8. Utilize Number Lines - Plot exact points for rationals and approximate spots for irrationals to see how they interweave. Visualizing numbers this way cements their relationships and reveals surprising gaps. Try a visualization activity
    9. Eighth Grade Compare and Order Rational and Irrational Numbers Worksheet
  9. Understand the Density Property - Between any two rationals lies another rational, and the same holds for irrationals, showcasing an infinite universe of numbers. Grasping this concept highlights the endless richness of the number line. Dive deeper into density
    10. Rational and Irrational Numbers Worksheet, Difference, and Examples
  10. Engage in Practice Quizzes - Regular, timed quizzes sharpen recall and speed, turning confusion into confidence before test day. Make mistakes here so you don't make them on an exam! Take a fun quiz
    11. Eighth Grade Rational and Irrational Numbers Quiz
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker