Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to distinguish between rational and irrational numbers and order real numbers containing roots.

Q1:

Which of the following is an irrational number that lies between 3 and 4?

Q2:

Which of the following is an irrational number that lies between − 7 and − 3 ?

Q3:

Arrange the numbers on the cards in ascending order.

Q4:

Is − 1 + √ 2 greater than, equal to, or less than − √ 2 + 1 ?

Q5:

A number has the infinite decimal expansion 0 . 4 5 4 4 5 4 4 4 5 4 4 4 4 5 . . . where the number of fours between the fives continues to increase. Is this a rational number?

Q6:

Which of the following is a rational number?

Q7:

Which of the following statements must be true, given that 𝑎 𝑏 is a rational number and 𝑎 𝑏 = 0 ?

Q8:

True or False? The quotient 𝑝 𝑞 where 𝑝 is an integer and 𝑞 is zero is a rational number.

Q9:

Simplify − 0 . 7 6 , giving your answer in the form 𝑎 𝑏 .

Q10:

A rational number is a number that can be written in the form 𝑎 𝑏 , where 𝑎 and 𝑏 are integers (whole numbers) and 𝑏 is not zero.

Q11:

Use ∈ or ∉ to complete the following: 𝜋 ℝ .

Q12:

Is every integer a rational number?

Q13:

Find three rational numbers lying between 1 7 and 5 6 .

Q14:

Which of the following fractions is numerically closest to 0 . 8 2 ?

Q15:

Is 0.456 a rational or an irrational number?

Q16:

What type of number is − 1 7 3 2 ?

Q17:

Given that 𝑐 ∈ ℚ and 1 3 𝑐 | 𝑐 | − 1 5 ∉ ℚ , what are the possible values of 𝑐 ?

Q18:

Find the rational number that equals 4 5 and the sum of its numerator and denominator equals 36.

Q19:

Which of the following is the smallest?

Q20:

Which of the following is an irrational number?

Q21:

Write the interval that represents the set of nonpositive real numbers.

Q22:

State whether the following statement is true or false: If 𝑎 and 𝑏 are positive, real numbers and 𝑎 > 𝑏 , then 𝑎 > 𝑏 2 2 .

Q23:

Every natural number is a real number.

Q24:

Is 𝜋 3 a rational or an irrational number?

Q25:

Write the interval representing the set of the positive real numbers ℝ + .

Don’t have an account? Sign Up