Rational Numbers & Irrational Numbers Quiz

1) Which of the following is irrational?

0.14

0.24014001400014…

0.14161416......

0.1416

The number 0.24014001400014… is irrational because it is a non-repeating and non-terminating decimal. Irrational numbers cannot be expressed as a fraction or a ratio of two integers, and they have an infinite number of non-repeating decimal places. Therefore, the number 0.24014001400014… cannot be expressed as a fraction and is considered irrational.

Explanation

The number 0.24014001400014… is irrational because it is a non-repeating and non-terminating decimal. Irrational numbers cannot be expressed as a fraction or a ratio of two integers, and they have an infinite number of non-repeating decimal places. Therefore, the number 0.24014001400014… cannot be expressed as a fraction and is considered irrational.

2) The decimal expansion of an irrational number may be

Terminating

Recurring

Either terminating or non- terminating

Non-terminating and non-recurring

An irrational number is a number that cannot be expressed as a fraction of two integers. The decimal expansion of an irrational number is non-terminating, meaning it goes on forever without repeating a pattern. Additionally, it is non-recurring, meaning there is no sequence of digits that repeats indefinitely. Therefore, the decimal expansion of an irrational number is both non-terminating and non-recurring.

Explanation

An irrational number is a number that cannot be expressed as a fraction of two integers. The decimal expansion of an irrational number is non-terminating, meaning it goes on forever without repeating a pattern. Additionally, it is non-recurring, meaning there is no sequence of digits that repeats indefinitely. Therefore, the decimal expansion of an irrational number is both non-terminating and non-recurring.

3) (16)^3/4 is equal to

2

4

8

16

The fraction 3/4 can be simplified by dividing the numerator (3) by the denominator (4). The result is 0.75, which can also be expressed as a whole number by multiplying it by 100. Therefore, 0.75 x 100 = 75. Since 75 is divisible by 8, the answer is 8.

Explanation

The fraction 3/4 can be simplified by dividing the numerator (3) by the denominator (4). The result is 0.75, which can also be expressed as a whole number by multiplying it by 100. Therefore, 0.75 x 100 = 75. Since 75 is divisible by 8, the answer is 8.

4) The square root of which number is rational

7

1.01

0.04

13

The square root of 0.04 is rational because it can be expressed as 0.2, which is a rational number.

Explanation

The square root of 0.04 is rational because it can be expressed as 0.2, which is a rational number.

5) 0.6666 in p/q form is

6/99

2/3

3/5

1/66

The decimal number 0.6666 can be expressed as a fraction in p/q form as 2/3.

Explanation

The decimal number 0.6666 can be expressed as a fraction in p/q form as 2/3.

6) On simplifying

we get

12

not-available-via-ai

Explanation

not-available-via-ai

7) The number

is

An irrational number

A rational number

Not a natural number

None of these

A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers. Since the question does not provide any specific number, it is not possible to determine if it is a rational number or not. Therefore, the answer "none of these" is the most appropriate.

Explanation

A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers. Since the question does not provide any specific number, it is not possible to determine if it is a rational number or not. Therefore, the answer "none of these" is the most appropriate.

8) The product of a rational and an irrational numbers is:

Always an integer

Always an irrational number

Always a rational number

Sometimes rational and sometimes irrational

When a rational number (a number that can be expressed as a fraction) is multiplied by an irrational number (a number that cannot be expressed as a fraction), the result is always an irrational number. This is because multiplying a rational number by an irrational number introduces new irrational components that cannot be simplified or expressed as a fraction. Therefore, the product of a rational and an irrational number is always an irrational number.

Explanation

When a rational number (a number that can be expressed as a fraction) is multiplied by an irrational number (a number that cannot be expressed as a fraction), the result is always an irrational number. This is because multiplying a rational number by an irrational number introduces new irrational components that cannot be simplified or expressed as a fraction. Therefore, the product of a rational and an irrational number is always an irrational number.

9) For rationalising the denominator of the expression

we multiply and divide by

12

To rationalize the denominator of an expression, we multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of the denominator is 12. By multiplying and dividing by 12, we can eliminate any irrational terms in the denominator and simplify the expression.

Explanation

To rationalize the denominator of an expression, we multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of the denominator is 12. By multiplying and dividing by 12, we can eliminate any irrational terms in the denominator and simplify the expression.

10) A rational number between

is

1/14

2/21

5/14

5/21

The given question asks for a rational number between two unspecified numbers. The answer, 5/21, is a rational number because it can be expressed as a fraction, with 5 as the numerator and 21 as the denominator. It is also between the other given rational numbers, 1/14 and 2/21, as it falls between them when arranged in ascending order.

Explanation

The given question asks for a rational number between two unspecified numbers. The answer, 5/21, is a rational number because it can be expressed as a fraction, with 5 as the numerator and 21 as the denominator. It is also between the other given rational numbers, 1/14 and 2/21, as it falls between them when arranged in ascending order.