# Worksheet: Rational and Irrational Numbers

In this worksheet, we will practice identifying and telling the difference between rational and irrational numbers.

**Q1: **

Is a rational or an irrational number?

- Aan irrational number
- Ba rational number

**Q2: **

What type of number is ?

- ARational
- BInteger
- CIrrational

**Q3: **

Is a rational or an irrational number?

- Aa rational number
- Ban irrational number

**Q4: **

All integers are numbers.

- Arational
- Birrational

**Q5: **

I have a number that cannot be expressed in the form where , and . Is this number rational or irrational?

- Airrational number
- Brational number

**Q6: **

Is 7 a rational or an irrational number?

- Aan irrational number
- Ba rational number

**Q7: **

Is a rational or an irrational number?

- Aa rational number
- Ban irrational number

**Q9: **

What type of number is ? Select all that apply.

- Ainteger
- Brational
- Cirrational

**Q10: **

What type of number is ? Select all that apply.

- Airrational
- Binteger
- Crational

**Q11: **

Is a rational or an irrational number?

- Aa rational number
- Ban irrational number

**Q12: **

What type of number is ? Select all that apply.

- Arational
- Binteger
- Cirrational

**Q13: **

Is a rational or an irrational number?

- Aan irrational number
- Ba rational number

**Q14: **

Is a rational or an irrational number?

- Aan irrational number
- Ba rational number

**Q15: **

Without using a calculator, order the numbers , , and from smallest to largest.

- A , , , , 12
- B , , , , 12
- C , , , 12,
- D12, , , ,
- E , , , 12,

**Q16: **

Without using a calculator, order the numbers 8, 7, and from smallest to largest.

- A
- B
- C
- D
- E

**Q17: **

On the number line, which arrow represents the value of ?

- Ab
- Bc
- Ca

**Q18: **

Benjamin wants to estimate the value of . He knows that is 3.14 to two decimal places but decides to round this to the nearest whole number to make this estimate easier to calculate.

What will his estimate of be?

Benjamin wants to check whether his approximation is accurate to the nearest whole number, so he rounds to 3.1. What will his approximation of be now?

Hence, what is an approximation of accurate to the nearest whole number?

**Q20: **

If a rational number is not a perfect square, will its square root be rational or irrational?

- Arational
- Birrational
- CIt could be either.

**Q21: **

What is ?

- A
- B
- C
- D

**Q22: **

What is ?

- A
- B
- C
- D