# Worksheet: Real Numbers

In this worksheet, we will practice distinguishing between rational and irrational numbers and representing real numbers on number lines.

**Q1: **

Every natural number is a real number.

- Anegative
- Bpositive

**Q2: **

Is a rational or an irrational number?

- Aan irrational number
- Ba rational number

**Q3: **

Is 0.456 a rational or an irrational number?

- Aa rational number
- Ban irrational number

**Q6: **

Which of the following is an irrational number?

- A
- B
- C59
- D
- E109.5

**Q7: **

Use or to complete the following:.

- A
- B

**Q8: **

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

- A
- B
- C

**Q9: **

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

- A
- B
- C
- D
- E

**Q11: **

Which of the following is a rational number?

- A
- B
- C
- D
- E

**Q12: **

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

- A,
- B,
- C,
- D,
- E,

**Q13: **

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

- Afalse
- Btrue

**Q14: **

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

Which of the following is a rational number?

- A
- B
- C
- D
- E

**Q15: **

Is every integer a rational number?

- Ano
- Byes

**Q16: **

Find three rational numbers lying between and .

- A
- B
- C
- D

**Q17: **

What type of number is ?

- Apositive rational
- Binteger
- Cnegative rational

**Q18: **

Given that and , what are the possible values of ?

- A
- B0
- C
- D13

**Q19: **

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

- A
- B
- C
- D
- E

**Q20: **

What is the union of the rational and irrational numbers?

- A
- B
- C
- D
- E

**Q21: **

Which of the following is a pair of rational numbers which lie between and ?

- A, 1
- B,
- C1,
- D,

**Q22: **

Which of the following is an irrational number?

- A
- B
- C
- D

**Q23: **

If , which of the following sets contains ?

- A
- B

**Q24: **

State whether the following is true or false: If and belong to , where , then .

- Afalse
- Btrue

**Q25: **

What is ?

- A
- B
- C
- D