**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

**Question 2 :**

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

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

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

**Question 3 : **

Why is the non terminating recurring decimal

2.0343434 .........

considered to be a rational number ? Explain.

**Question 4 : **

Is √26 rational or irrational number ?

Explain your answer.

**Question 5 :**

Can 2.0342536901 ......... 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

**Answer :**

**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.......................

**Answer : **

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.

Because 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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