How is v5 represented on a number line?

Construct a right triangle with sides 2 units and 1 unit; the hypotenuse equals v5 when placed on the number line.

What is the use of the Euclid Division Algorithm?

It is used to compute the highest common factor (HCF) of two given numbers.

What is the importance of number systems?

Number systems help perform calculations, comparisons, and quantitative measurements efficiently.

What are laws of rational exponents?

Laws include: a^(1/n) = nva and a^(m/n) = (nva)^m.

What is the meaning of exponent with negative power?

A negative exponent means reciprocal of the base raised to the positive exponent, e.g., a?n = 1/an.

What is meant by representation of real numbers on a number line?

It means plotting each real number at a specific position corresponding to its value on a line.

Are integers closed under division?

No, dividing two integers may not always result in an integer, e.g., 3 ÷ 2 = 1.5.

How can we identify if a number is rational or irrational?

If a number can be expressed as p/q, it’s rational; otherwise, it’s irrational.

What are examples of irrational numbers?

Examples include v2, v3, p, and e, which have non-repeating, non-terminating decimals.

What is the decimal number system?

The decimal system is a base-10 system using digits from 0 to 9, most commonly used in mathematics.

What is the binary number system?

The binary system is a base-2 system using only 0 and 1, commonly used in computers.

What is meant by base in number systems?

The base is the number of unique digits used to represent numbers in a system. For example, base 10 uses digits 0–9.

What are non-terminating repeating decimals?

Rational numbers whose denominators (in lowest form) have prime factors other than 2 or 5 give non-terminating repeating decimals.

What are terminating decimals in rational numbers?

Terminating decimals are rational numbers whose denominators (in lowest form) have prime factors 2, 5, or both.

What is the HCF and LCM relationship?

For two numbers a and b, HCF × LCM = a × b.

How is Euclid’s lemma used to find HCF?

By repeatedly applying a = bq + r, the last non-zero remainder gives the HCF of two numbers.

What is Euclid’s division lemma?

Euclid’s division lemma states that for any integers a and b, there exist unique integers q and r such that a = bq + r, where 0 = r < b.

What are composite numbers?

Composite numbers have more than two factors, such as 4, 6, 8, and 9.

What are prime numbers?

Prime numbers are natural numbers greater than 1 that have only two factors — 1 and the number itself.

What is the difference between a number and a numeral?

A number represents quantity or value, while a numeral is the symbol used to express that number.

What is the use of real numbers in daily life?

Real numbers are used in measurement, money, temperature, and scientific calculations involving both rational and irrational values.

Is p a rational number?

No, p is an irrational number because its decimal expansion is non-terminating and non-repeating.

Are all terminating decimals rational?

Yes, all terminating decimals can be expressed as fractions, so they are rational.

Do irrational numbers satisfy closure under addition?

No, the sum of two irrational numbers may or may not be irrational (e.g., v2 + (-v2) = 0).

Do rational numbers satisfy the closure property under addition?

Yes, the sum of two rational numbers is always a rational number.

What is meant by the closure property?

Closure property states that the result of an operation on numbers in a set remains within that set.

What is the relationship between natural, whole, and integers?

Natural ? Whole ? Integers — meaning each set is contained in the next larger one.

Surds are irrational numbers that can be expressed in root form, such as v2, v3, and v5.

What is the standard form of a rational number?

A rational number is in standard form when its denominator is positive, and the numerator and denominator have no common factors except 1.

Can zero be considered a rational number?

Yes, 0 is a rational number because it can be expressed as 0/1.

What is a number line used for?

A number line visually represents all real numbers in order, showing their relative positions.

What is the product of a number and its reciprocal?

The product of a number and its reciprocal is always 1.

What is the value of a° for any non-zero number a?

For any non-zero number, a° = 1.

What are the laws of exponents for real numbers?

The laws of exponents include: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m-n), (a^m)^n = a^(mn), and a^0 = 1.

What is a terminating decimal?

A terminating decimal has a finite number of digits after the decimal point, like 0.5 or 0.125.

What is a repeating or recurring decimal?

A repeating decimal has digits that repeat in a pattern, for example, 0.666… or 0.142857142857…

What is the meaning of non-terminating decimal?

A non-terminating decimal continues infinitely without ending, like 0.333... or 0.142857142857...

How do you locate v2 on a number line?

Construct a right-angled triangle with both legs of 1 unit each; the hypotenuse represents v2 when plotted on the number line.

What is the difference between real and rational numbers?

All rational numbers are real, but not all real numbers are rational. Real numbers include both rational and irrational types.

Can every real number be represented on a number line?

Yes, every real number, whether rational or irrational, can be represented on the number line.

What is the decimal expansion of irrational numbers?

The decimal expansion of irrational numbers is non-terminating and non-repeating.

What is the decimal expansion of rational numbers?

The decimal expansion of rational numbers is either terminating or non-terminating repeating.

Integers include all whole numbers and their negatives, such as … -3, -2, -1, 0, 1, 2, 3 …

What are whole numbers?

Whole numbers include all natural numbers and 0, i.e., 0, 1, 2, 3, 4, ...

What are natural numbers?

Natural numbers are counting numbers starting from 1, 2, 3, and so on.

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as p/q, while irrational numbers cannot. Rational decimals terminate or repeat; irrational decimals do not.

What are irrational numbers?

Irrational numbers cannot be written as a simple fraction and have non-terminating, non-repeating decimals, like v2 or p.

What are rational numbers?

Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and \(q \neq 0.\)

What are real numbers in Class 9?

Real numbers include both rational and irrational numbers that can be represented on the number line.

What is a number system in mathematics?

A number system is a way of expressing numbers using symbols and rules. It includes natural numbers, whole numbers, integers, rational, and irrational numbers.

Number Systems MCQs – NCERT Class 9 Maths Chapter 1

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