Real Numbers Quiz - CBSE Class 10 Mathematics
Free practice quiz: Real Numbers (CBSE Class 10 Mathematics). 15 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
This CBSE Class 10 Mathematics practice quiz has 15 multiple-choice questions on Real Numbers, and 15 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.
Start quiz: 15 questions, freeAbout this topic
Real numbers (mathbbR) include natural, whole, integers, rational and irrational numbers. Every real number is a point on the number line, and every point is a real number. Rational numbers have terminating or non-terminating repeating decimals; irrational numbers have non-terminating non-repeating decimals.
- Natural numbers N = 1, 2, 3, …; whole numbers W = 0, 1, 2, … (0 is the least whole number).
- Integers Z = …, −2, −1, 0, 1, 2, …; every whole number is an integer.
- Rational number: can be written as p/q with p, q integers and q ≠ 0. Example: 3/4, 1.25 = 5/4.
- Rational decimals either terminate (like 1.25) or repeat forever (like 1/3 = 0.333…).
- Irrational numbers have non-terminating, non-repeating decimals. Examples: √2, √3, π.
- Real numbers = rational + irrational. Order of sets: N subset W subset Z subset Q subset R.
- Between any two real numbers there are infinitely many rational and irrational numbers.
Learn the key ideas Beta
Number sets and how they nest
- Natural numbers are counting numbers. Whole numbers add the additive identity, the number a with a + x = x.
- Integers add the negatives of natural numbers. Every integer is rational, and every rational number is real.
- A number belongs to every larger set containing its own set. Decimals and fractions in lowest form with denominator other than ±1 are not integers.
Common mistake: Thinking negative numbers are whole numbers, or forgetting that the smallest whole number has no whole-number predecessor.
Rational numbers as fractions
- A rational number can be written as p/q, where p and q are integers and q is not zero.
- Every integer n is rational because it can be written as n/1.
Common mistake: Believing fractions like 5/7 are not real numbers. Every rational number is also a real number.
Irrational numbers
- An irrational number cannot be written as p/q with integers p and q, q not zero.
- Square roots of non-perfect squares, like √5 or √7, and π are irrational.
Common mistake: Assuming the product or sum of two irrational numbers is always irrational. It may be rational or irrational.
Decimal expansions decide the type
- Rational numbers have decimals that either terminate or repeat forever in a fixed block.
- Irrational numbers have decimals that never terminate and never repeat a block, for example 0.101001000100001…
Common mistake: Calling a non-terminating decimal irrational even when it repeats. Repeating decimals are always rational.
Properties of every real number
- Every real number a has an additive inverse -a, which is also a real number.
- Every real number is either rational or irrational, never both. Each one sits on the number line.
Common mistake: Thinking -a must be negative. If a is negative, then -a is positive.
Exam tips
- Before choosing an answer, place the number in the smallest set it belongs to.
- For fractions, reduce to lowest form first, then factor the denominator to check if it terminates.
- Watch for words like 'always', 'never' and 'not' in true or false statements.
Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.
Sample questions
What are the set of all real numbers?
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Answer: C. Real numbers
Real numbers include both rational and irrational numbers, encompassing all numbers without imaginary components.
Which number is not a whole number?
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Answer: C. 7.5
Whole numbers are all non-negative integers, 7.5 has a fractional part which makes it not a whole number.
What is the least whole number?
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Answer: A. 0
0 is the smallest whole number because whole numbers start from 0.
Which is true for every real number?
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Answer: C. It is real
Every number classified in this range of study is indeed a real number.
The product of two irrational numbers is:
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Answer: C. Sometimes rational
Product of two irrational numbers can be rational, for example: √2 * √2 = 2.
More questions in this quiz
Answers and explanations are in the full quiz.
- Is the number 3 an integer?
- Which of these numbers is irrational?
- The number 3/4 is a:
- A number that cannot be expressed as a fraction is:
- Which statement is true about integers?
- Which whole number has no predecessor?
- Among these, choose the rational number representation.
- Identify which of these is not an integer.
- Which statement about real numbers is false?
- For any real number 'a', the number -a is:
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