Question

Which of the following rational number is between 1 and 2? निम्नलिखित में से कौन सी तर्कसंगत संख्या 1 और 2 के बीच है? *
1 point

Option 1

Option 2

Option 3

Option 4
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Answer 1

Which of the following rational number is between 1 and 2?

Step-by-step explanation:

• There are indefinite rational numbers between two integers.

• To Find: Rational number lies between 1 & 2

• The rational number between a and b is (a + b)/2

• Hence rational number between 1 and 2 is

                              ⇒(1+2)/2 = 3/2 = 1.5

               ⇒1 and 3/2 is [1+(3/2)]/2 = 5/4 = 1.25

               ⇒1 and 5/4 is [1+(5/4)]/2 = 9/8 = 1.125

               ⇒ 3/2 and 2 is [(3/2) + 2]/2 = 7/4= 1.75

• Here are four rational numbers between 1 and 2 - 1.5, 1.25, 1.125, 1.75

• Therefore, there can be indefinite rational numbers between any two integers.

Answer 2

SOLUTION

CORRECT QUESTION

Which of the following rational number is between 1 and 2? निम्नलिखित में से कौन सी तर्कसंगत संख्या 1 और 2 के बीच है?

Option 1. 7/4

Option 2. 2/7

Option 3. 1/3

Option 4. 12/5

EVALUATION

We know that between two rational numbers there are infinite number of rational numbers

Here we write 1 and 2 as below

$\displaystyle \sf{1 = \frac{4}{4} }$

$\displaystyle \sf{2 = \frac{8}{4} }$

Now

$\displaystyle \sf{ \frac{4}{4} < \frac{7}{4} < \frac{8}{4} }$

$\implies \displaystyle \sf{ 1< \frac{7}{4} < 2 }$

Hence the correct option is

$\displaystyle \sf{1. \: \: \: \: \frac{7}{4} }$

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