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Quizzes > Mathematics > Basic Math & Arithmetic

Number System Quiz: Test Your Math Mastery

Challenge Yourself with a Math Number System Test on Rational & Irrational Numbers

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper cut numbers fractions equation symbols layered on dark blue background for number system quiz challenge

Get ready to boost your confidence with our free number system quiz designed to challenge and educate! In this math number system test, you'll dive into rational and irrational puzzles and tackle fractions in a supportive, engaging format. Perfect for students and lifelong learners, this quiz blends basic number system questions with stimulating challenges to identify your strengths and gaps. Explore a sample rational and irrational numbers quiz and sharpen your skills through our interactive fraction quiz . Take the plunge now and see how you measure up - you've got this!

Which of the following is a rational number?
3/7
?
e
?2
A rational number can be expressed as the ratio of two integers. The number 3/7 is exactly a ratio of integers 3 and 7 and thus rational. Numbers like ?2, ?, and e cannot be expressed as such ratios and are irrational. Math is Fun - Rational Numbers
Which decimal is a terminating decimal?
0.333...
0.125
0.666...
0.285714...
A terminating decimal has a finite number of digits after the decimal point. The decimal 0.125 stops after three digits, making it a terminating decimal. Repeating decimals like 0.333... or 0.666... continue indefinitely. Math is Fun - Terminating Decimals
What is the decimal equivalent of the binary number 1010?
12
8
10
9
In binary, the place values from right to left are 1, 2, 4, and 8. The binary number 1010 represents 1*8 + 0*4 + 1*2 + 0*1 = 10 in decimal. Math is Fun - Binary Numbers
Which set of numbers includes negative numbers, zero, and positive numbers?
Real numbers
Whole numbers
Natural numbers
Integers
Integers include negative whole numbers, zero, and positive whole numbers. Natural numbers are only positive, and whole numbers include zero and the positives but not negatives. Real numbers include all rationals and irrationals, but the more precise answer for this classification is integers. Math is Fun - Integers
The number ? (pi) is classified as which type of number?
Rational number
Imaginary number
Integer
Irrational number
? is an irrational number because it cannot be expressed as a ratio of two integers and has a non-repeating, non-terminating decimal expansion. It is not an integer or imaginary. Math is Fun - Pi
What is the simplified form of the fraction 15/35?
5/7
1/3
7/15
3/7
To simplify 15/35, divide numerator and denominator by their greatest common divisor, which is 5. That gives 15÷5 = 3 and 35÷5 = 7, so the simplified form is 3/7. Math is Fun - Reducing Fractions
Which of the following is NOT a real number?
0
-3/4
2.5
?(-1)
Real numbers include all rational and irrational numbers. ?(-1) is not a real number because it involves the square root of a negative, which is an imaginary number (often denoted i). Math is Fun - Real Numbers
How is the number 7 represented in base 5?
17
13
12
21
In base 5, the place values are 1, 5, 25, etc. To represent 7, you use one 5 and two 1s: 1*5 + 2*1 = 7, so it is written as 12 in base 5. Math is Fun - Number Bases
Convert 0.222... (repeating) to a fraction.
1/9
1/6
1/5
2/9
Let x = 0.222... then 10x = 2.222..., subtracting gives 9x = 2, so x = 2/9. This method converts the repeating decimal to a fraction. Khan Academy - Repeating Decimals
Which of the following is an irrational number?
?4
2.75
9/16
?2
?2 cannot be expressed as a ratio of two integers and its decimal expansion never terminates or repeats, making it irrational. ?4 equals 2, and the others are rational. Math is Fun - Irrational Numbers
What is the least common multiple of 12 and 18?
90
36
72
54
The prime factors of 12 are 2^2 * 3, and of 18 are 2 * 3^2. Taking the highest powers gives 2^2 * 3^2 = 4 * 9 = 36 as the LCM. Math is Fun - LCM
In hexadecimal, the digit 'A' represents what decimal value?
15
11
12
10
Hexadecimal is base 16, using digits 0 - 9 and letters A - F. 'A' corresponds to decimal 10. Math is Fun - Hexadecimal
Which decimal number is repeating?
0.625
0.75
0.121212...
0.142
A repeating decimal has a block of digits that repeat indefinitely. 0.121212... has '12' repeating, whereas the others terminate or do not have a repeating pattern. Math is Fun - Repeating Decimals
Which fraction equals 0.625?
7/16
1/3
3/4
5/8
0.625 = 625/1000. Simplifying by dividing numerator and denominator by 125 gives 5/8. Math is Fun - Converting Decimals & Fractions
The number zero (0) is part of which number set?
Whole numbers
Natural numbers
Rational numbers
Integers
Whole numbers are defined as the set {0, 1, 2, 3, ...}. Natural numbers typically start at 1, though conventions vary. Integers and rational numbers include zero but are broader sets. Math is Fun - Whole Numbers
Which of these sets is NOT closed under multiplication?
Whole numbers
Rational numbers
Integers
Irrational numbers
Closure under multiplication means the product of any two members stays in the set. Multiplying some irrationals (e.g., ?2 × ?2) can yield a rational result, so the set of irrationals is not closed under multiplication. Wikipedia - Closure
Convert the binary number 110.11 to its decimal equivalent.
7.25
6.5
6.75
7.5
110.11? = 1×4 + 1×2 + 0×1 + 1×½ + 1×¼ = 6 + 0.5 + 0.25 = 6.75. Math is Fun - Binary Numbers
What is the sum of the infinite series 1/2 + 1/4 + 1/8 + ... ?
1
Infinity
1/2
2
This is a geometric series with first term a = 1/2 and ratio r = 1/2. The sum is a/(1?r) = (1/2)/(1/2) = 1. Khan Academy - Geometric Series
What is the decimal expansion of 3/7?
0.142857142857...
0.285714285714...
0.428571428571...
0.571428571428...
Dividing 3 by 7 gives a repeating block '428571'. Hence 3/7 = 0.428571428571... Math is Fun - Fractions & Decimals
In base 8, what is the decimal value of 17?
9
15
17
14
In base 8, 17? = 1×8 + 7 = 15 in decimal. Math is Fun - Number Bases
Which of these sets is uncountable?
Rational numbers
Real numbers
Natural numbers
Integers
The set of real numbers cannot be put into a one-to-one correspondence with the naturals, making it uncountable. The others are countable sets. Wikipedia - Countable Set
Which of the following is an irrational number?
0.121212...
0.25
0.101001000100001...
0.111000111000...
0.101001000100001... has no repeating pattern and is non-terminating, so it is irrational. The others either repeat or terminate, making them rational. Math is Fun - Irrational Numbers
Express 56,000 in scientific notation.
5.6×10^4
56×10^3
560×10^2
0.56×10^5
56,000 = 5.6 × 10^4 since you move the decimal 4 places to the left to get a number between 1 and 10. Math is Fun - Scientific Notation
What is the greatest common divisor (GCD) of 48 and 180?
6
12
24
18
48 = 2^4×3, 180 = 2^2×3^2, so the common factors are 2^2×3 = 4×3 = 12. Math is Fun - GCD
According to the Gelfond - Schneider theorem, how is 2^?2 classified?
Algebraic irrational
Algebraic integer
Transcendental number
Rational number
The Gelfond - Schneider theorem states that 2^?2 is a transcendental number (not algebraic). This is a classic result in transcendence theory. Wikipedia - Gelfond - Schneider Theorem
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Study Outcomes

  1. Understand Number Set Classifications -

    Recognize and categorize numbers into natural, whole, integer, rational, and irrational sets to build foundational number system knowledge.

  2. Differentiate Rational and Irrational Numbers -

    Identify characteristics of rational and irrational numbers and distinguish between them through targeted quiz questions.

  3. Convert Between Fractions and Decimals -

    Apply conversion techniques to translate fractions into decimals and decimals into fractions accurately.

  4. Apply Fundamental Number Properties -

    Utilize properties like commutativity, associativity, and distributivity when solving number system problems.

  5. Analyze Number Line Positions -

    Plot and compare numbers on the number line to determine their relative values and order.

  6. Evaluate Square Roots and Perfect Squares -

    Calculate square roots of perfect squares and recognize non-perfect squares to deepen understanding of the number system.

Cheat Sheet

  1. Hierarchy of Number Sets -

    Understanding how natural numbers (ℕ), whole numbers, integers (ℤ), rational numbers (ℚ), and irrational numbers together form the real numbers (ℝ) is foundational. For example, 5∈ℕ⊂ℤ⊂ℚ⊂ℝ, but √2∉ℚ, so √2∈ℝ - ℚ. Visualizing these nested sets can simplify many basic number system questions.

  2. Rational Numbers and Decimal Patterns -

    Rational numbers are fractions a/b (b≠0) whose decimal expansions either terminate (e.g., ¾=0.75) or repeat (e.g., 1/7≈0.142857…). As noted by Khan Academy, spotting these patterns quickly helps you excel on math number system tests. Use a repeating”bar notation (0.\overline) to track cycles during number system practice quizzes.

  3. Identifying Irrational Numbers -

    Irrational numbers cannot be written as simple fractions and exhibit non-terminating, non-repeating decimals (e.g., π≈3.14159…, √2≈1.41421…). According to MIT OpenCourseWare, decimals that never repeat or end are clear identifiers in a rational and irrational numbers quiz. A quick mnemonic "No Repeat, No Rest" can help you recall their decimal behavior.

  4. Converting Between Fractions, Decimals, and Percentages -

    To convert a fraction to a decimal, divide the numerator by the denominator (e.g., 3 ÷ 8 = 0.375), then multiply by 100 to get a percentage (0.375×100=37.5%). Per Pearson's Math Essentials, mastering these conversions is crucial for any number system quiz. Regular practice with varied examples will boost your speed and confidence in number system practice quizzes.

  5. Prime Factorization and Divisibility Rules -

    Breaking numbers into primes (e.g., 60=2²×3×5) simplifies finding GCD and LCM for many basic number system questions. Divisibility shortcuts - like checking the sum of digits for 3 and 9 or the last two digits for 4 - are fast checks endorsed by Wolfram MathWorld. Learning these tricks will give you an edge in every math number system test or number system practice quiz.

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