Grade 9 Maths Number System (Part A)

Every rational number is

• a natural number

• an integer

• a real number

• a whole number

Answer explanation

Every rational number is a real number, as rational numbers can be expressed as fractions and fall within the set of real numbers.

Decimal representation of a rational number cannot be

• terminating

• non-terminating

• non-terminating repeating

• non-terminating non-repeating

Answer explanation

Decimal representation of a rational number cannot be non-terminating non-repeating, as rational numbers have either terminating or non-terminating repeating decimal representations.

• terminating

• non-terminating

• non-terminating repeating

• non-terminating non-repeating

Answer explanation

The correct choice is 'non-terminating non-repeating' because the decimal expansion of pi goes on indefinitely without repeating a pattern.

Every point on a number line represents

• a unique real number

• a natural number

• a rational number

• an irrational number

Answer explanation

Every point on a number line represents a unique real number, making it the correct choice.

Which of the following is a rational number?

Answer explanation

The rational number is a number that can be expressed as a fraction. Among the given choices, -2/3 is a rational number because it can be written as a fraction of two integers.

Which of the following is irrational?

• 0.15

• 0.5015001500015...

Answer explanation

The irrational number is 0.5015001500015... because it has a non-repeating and non-terminating decimal expansion, unlike the other options.

Answer explanation

To find a rational number equivalent to 3/17, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1. Therefore, 3/17 is equivalent to 3/17 * 2/2 = 6/34.

A rational number between 2 and 3 is

• 2.010010001...

Answer explanation

The rational number between 2 and 3 is 2.5, which is represented as \frac{5}{2}.

Four rational numbers between 3 and 4 are

• 3.1, 3.2, 3.8, 3.9

• 3.1, 3.2, 4.1, 4.2

Answer explanation

The correct answer is 3.1, 3.2, 3.8, 3.9 as they are rational numbers between 3 and 4.

Answer explanation

To get a rational number, the irrational part must cancel out. Adding -√2 to 3+√2 results in 3+√2-√2 = 3, which is rational.