**Classifying rational numbers worksheet:**

Worksheet on classifying rational numbers is much useful to the students who are at the stage of learning rational numbers.

1. Place the following numbers in the Venn diagram. Then classify each number by indicating in which set or sets each number belongs.

0.35, -3, 75, 3/4

2. Classify the following two numbers as rational and irrational and also explain your answer.

5.312312312.......................

5.385164807.......................

3. Why is the non terminating recurring decimal

2.0343434 .........

considered to be a rational number ? Explain.

3. Why is the non terminating recurring decimal

2.0343434 .........

considered to be a rational number ? Explain.

4. Is √26 rational or irrational number ?

Explain your answer.

5. Can 2.0342536901 ......... be written as a fraction ?

If yes, write the given number as a fraction.

If no, explain why it can not be written as a fraction.

**Question 1 : **

Place the following numbers in the Venn diagram. Then classify each number by indicating in which set or sets each number belongs.

0.35, -3, 75, 3/4

**Solution :**

**75 : **

The number 75 belongs in the sets of whole numbers, integers, and rational numbers.

**-3 :**

The number -3 belongs in the sets of integers and rational numbers.

**3/4 :**

The number -3/4 belongs in the set of rational numbers.

**0.35 :**

The number 0.35 belongs in the set of rational numbers.

**Question 2 :**

Classify the following two numbers as rational and irrational and also explain your answer.

5.312312312.......................

5.385164807.......................

**Solution : **

5.312312312....................... ---> Rational number

5.385164807....................... ---> Irrational number

**Explanation : **

Even though 5.312312312.......... is a non terminating decimal, there is a repeated pattern 312 in it.

So, 5.312312312....... is non terminating recurring decimal.

Hence, 5.312312312....... is a rational number.

5.385164807............ is a non terminating decimal and also there is no repeated pattern in it.

So, 5.385164807............ is non terminating non recurring decimal.

Hence, 5.385164807............ is an irrational number.

**Question 3 : **

Why is the non terminating recurring decimal

2.0343434 .........

considered to be a rational number ? Explain.

**Solution : **

Rational number is usually expressed in the form a/b.

So, if we can express any number in the form "a/b", the number can be considered as rational number.

Now, let us see, how to express the number 2.0343434...... in the form a/b, say fraction.

**Step 1 : **

Let x = 2.0343434...........

**Step 2 : **

Identify the repeated pattern

In 2.0343434..........., the repeated pattern is 34

(Because 34 is being repeated)

**Step 3 :**

Identify the first repeated pattern and second repeated pattern as as explained below.

**Step 4 :**

Count the number of digits between the decimal point and first repeated pattern as given in the picture below.

**Step 5 :**

Since there is 1 digit between the decimal point and the first repeated pattern, we have to multiply the given decimal by 10 as given in the picture below.

(If there are two digits -----------> multiply by 100,

three digits -----------> multiply by 1000 and so on )

Note : In (1), we have only repeated patterns after the decimal.

**Step 6 : **

Count the number of digits between the decimal point and second repeated pattern as given in the picture below.

**Step 7 :**

Since there are 3 digits between the decimal point and the second repeated pattern, we have to multiply the given decimal by 1000 as given in the picture below.

Note : In (2), we have only repeated patterns after the decimal.

**Step 8 :**

Now, we have to subtract the result of step 5 from step 7 as given in the picture below.

Now we got the fraction which is equal to the given decimal.

Since the given non terminating recurring decimal can be written as a fraction, it is considered to be a rational number.

**Question 4 : **

Is √26 rational or irrational number ?

Explain your answer.

**Solution : **

√26 is an irrational number.

Because, when we find square root of 26, we get a non terminating non recurring decimal.

That is,

√26 = 5.0990195..........

Hence, √26 is an irrational number.

**Question 5 : **

Can 2.0342536901 ......... be written as a fraction ?

If yes, write the given number as a fraction.

If no, explain why it can not be written as a fraction.

**Solution : **

No, 2.0342536901 ......... can not be written as a fraction.

Because, 2.0342536901 ......... is a non terminating non recurring decimal.

**Note :**

Only non terminating recurring decimal can be written as a fraction.

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