# 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

Q8:

According to the US Mint, the diameter of a quarter is 0.955 inches. The circumference of the quarter would be the diameter multiplied by . Is the circumference of a quarter a whole number, a rational number, or an irrational number?

• Arational number
• Birrational number
• Cwhole 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:

Mason 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?

Mason 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?

Q19:

Without using a calculator, order the numbers , , 1, 2, and from smallest to largest.

• A, , 2, , 1
• B1, , 2, ,
• C1, , , 2,
• D, 1, , 2,
• E, 2, , , 1

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

Q23:

Which of the following is an irrational number that lies between 2 and 3?

• A
• B
• C2.6
• D
• E

Q24:

A square of side length cm has an area of 280 cm2. Which of the following is true about ?

• AIt is an integer number.
• BIt is an irrational number.
• CIt is a negative number.
• DIt is a natural number.
• EIt is a rational number.