Rational Numbers | MCQs

Explanation

Given a and b are integers and b ≠ 0:

a/b represents a Rational number.

A rational number is a number that can be expressed as the ratio of two integers, where the denominator is non-zero.

Explanation

The product of two rational numbers is always rational because the product of two fractions (or integers) is another fraction (or integer).

Rational numbers are closed under multiplication, meaning multiplying two rationals results in another rational number.

Explanation

0.75 is a terminating decimal, which can be written as 75/100.

Simplifying 75/100 gives 3/4, making it a rational number.

Explanation

A rational number is a number that can be written as a fraction (p/q) where p and q are integers and q ≠ 0.

3/0 is a rational number.

Explanation

A rational number is defined as a number that can be expressed as the ratio of two integers, i.e., a/b, where a and b are integers and b ≠ 0.

Every rational number can be written in the form of a fraction, where the numerator and denominator are integers.

Example: 3/4, 22/7, 1/2, etc.

Explanation

The correct definition of rational numbers is:

The set of all numbers of the form p/q where p and q are integers and q ≠ 0.

This is because rational numbers are defined as the ratio of two integers, with the denominator (q) being non-zero.

Explanation

The reciprocal of a number x is 1/x.

0 has no reciprocal because 1/0 is undefined.

Explanation

In negative fractions, the greater the denominator (for the same numerator), the closer the fraction is to zero, making it larger.

Comparing:

• -1/3 = -0.333
• -2/3 = -0.666
• -4/9 = -0.444
• -5/6 = -0.833

-1/3 is the greatest among them as it is closest to zero.

Explanation

The set $left{frac{p}{q} : p, q in mathbb{Z}, q neq 0right}$ represents the set of rational numbers.

Rational Numbers: A number is considered rational if expressed as the quotient $frac{p}{q}$, where $p$ and $q$ are integers and $q\mathrm{\ne }0$

This set includes numbers like $frac{1}{2}$, $-frac{3}{4}$, and $7$ (which can be written as $frac{7}{1}$).

Explanation

A rational number can be written as a fraction (p/q) with both p and q as integers.

All given options are irrational:

3.129765917723... is non-repeating, non-terminating

π and √2 are well-known irrational numbers.