CLASSIFY RATIONAL AND IRRATIONAL NUMBERS WORKSHEET

Classify each number as RATIONAL (Q) or IRRATIONAL (I)

Problem 1 :

√47

Solution

Problem 2 :

11/9

Solution

Problem 3 :

19/4

Solution

Problem 4 :

√96

Solution

Problem 5 :

19/14

Solution

Problem 6 :

15/4

Solution

Problem 7 :

√84

Solution

Problem 8 :

-9

Solution

Problem 9 :

√72

Solution

Problem 10 :

0

Solution

Problem 11 :

8/9

Solution

Problem 12 :

Which statement is not always true?

1) The product of two irrational numbers is irrational.

2) The product of two rational numbers is rational.

3) The sum of two rational numbers is rational. 

4) The sum of a rational number and an irrational number is irrational.

Solution

Problem 13 :

Determine if the product of 3√2 and 8 √18 is rational or irrational ? Explain your answer.

Solution

Problem 14 :

Which of the following numbers is irrational?

a) 0.252525…     b) 0.875       c) 0.3754152…     d) -0.121212… 

Solution

Problem 15 :

The product of any two irrational numbers is:

a) always an irrational number           b) always a rational number

c) always an integer             d) sometimes rational, sometimes irrational

Solution

Problem 16 :

Between two rational numbers:

a) there is no rational number          b) there is exactly one rational number

c) there are infinitely many rational numbers

d) there are only rational numbers and no irrational numbers

Solution

Problem 17 :

If a = -2 , b = -1, then find 𝑎^−𝑏 − 𝑏^𝑎.

Solution

Problem 18 :

Find the three rational numbers between:

(i) -1 and -2

(ii) 0.1 and 0.11

Solution

Problem 1 :

Which irrational numbers is between 4 and 5.

a. √12    b.√20    c. √34     d. √80

Solution

Problem 2 :

Which number is an integer ?

a. -11/5    b.-7    c. √15     d. 1/2

Solution

Problem 3 :

Which number is irrational ?

a. 9.2727....    b.√2    c. 5√9     d. -37/71

Solution

Problem 4 :

Which of the following is a rational number but is NOT an integer?

a. 8     b. 24      c. 40/4     d. 6.2

Solution

Problem 5 :

Barbara was asked to create a set of numbers that contained only integers. Which of the sets does NOT contain only integers?

a. {11, 6, -3, -4, 600, 24/12}

b. {9, 100, -4, 12, -6, 20/5}

c. {5, 3, -8, -14, 3.5, 24/12}

d. {22, -12.0, 9, -14, 28, 4}

Solution

Problem 6 :

Rational numbers are a dense set. This means that between any two rational numbers on a number line there is another rational number. Which rational number is between 2.46 and 2.47 on a number line?

a. 2.48   b. G 2.4   c. 2.53    d. 2.468

Solution

Problem 7 :

Which statement is NOT true about rational numbers?

a. The sum of two rational numbers is also a rational number.

b. 0 is not a rational number.

c. The product of two rational numbers is also a rational number.

d. The opposite of a rational number is also a rational number.

Solution

Problem 8 :

i) √40 has an infinite non repeating decimal expansion.

ii)  The number 0.5656...... is a rational number.

iii)  -200 and 500 are integers

iv)  All numbers with infinite decimal expansions are irrational.

v)  The numbers -8, -3, 5, 17 are all whole numbers.

Solution

Problem 9 :

Which number is irrational

a. 9.2727.....      b.√2         c. 5√9       d.-37/71

Solution

Problem 10 :

Any number with a finite decimal expansion must be 

a. rational    b. irrational

Solution

Problem 11 :

All integers are 

a.  Whole      b. rational    c. irrational

Solution

Problem 12 :

For what value of P and W is P + W a rational number ?

a.  P = 1/√3 and W = 1/√6               b. P = 1/√4 and W = 1/√9

c. P = 1/√6 and W = 1/√10               d. P = 1/√25 and W = 1/√2

Solution

Problem 1 :

Which of these are rational?

a. 8     b. -8     c. 2 1/3     d. -3 1/4

e. √3    f. √400     g. 9.176     h. π - π

Solution

Problem 2 :

Show that these numbers are rational:

a. 0.7.....       b. 0.41.....       c. 0.324.......

Solution

Problem 3 :

a. Why is 0.527 a rational number?

b. 0.9 is a rational number. In fact, 0.9 € Z. Give evidence to support this statement.

Solution

Problem 4 :

Explain why these statements are false:

a. The sum of two irrationals is irrational.

b. The product of two irrationals is irrational.

Solution

Problem 5 :

a. Explain why 1.3 is a rational number.

b. True or false. √4000 € Q ?

Solution

Problem 6 :

a. True or false: 1/√7 € Q ?

b. Show that 0.41 is a rational number.

Solution

Problem 7 :

Is the sum of 3√2 and 4√2 rational or irrational 

Solution

Problem 8 :

Jacob is working on his math homework. He decides that the sum of the expression 1/3 + 6√5/7 must be rational because it is fraction. Is Jacob correct ?

Solution

Problem 9 :

State whether 7 - √2 is rational or irrational

Solution

Problem 10 :

Is the product of √16 and 4/7 rational or irrational ?

Solution