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Question

Answers

A.\[0.75\], \[0.7\], \[0.76\]

B.\[0.75757575\],\[0.7\], \[0.76\]

C.\[0.75075007500075000075...\], \[0.7670767007670007670000767...\], \[0.808008000800008...\]

D.None of these

Answer
Verified

We are given the rational numbers \[\dfrac{5}{7}\] and \[\dfrac{9}{{11}}\].

We know that the rational numbers are those numbers which can be written in the form of \[\dfrac{p}{q}\], where \[p\] is numerator, \[q\] is denominator, \[q \ne 0\] and both are integers.

We also know that irrational numbers are numbers that can not be represented in the rational number form, they are non-recurring and non-terminating decimal numbers.

Rewriting the rational number \[\dfrac{5}{7}\] into decimal form, we get

\[ \Rightarrow \dfrac{5}{7} = 0.714285714285714285...\]

Rewriting the rational number \[\dfrac{9}{{11}}\] into decimal form, we get

\[ \Rightarrow \dfrac{9}{{11}} = 0.81818181...\]

Considering option A,

Since the three numbers are terminating rational numbers and \[0.7\] does not lie between the two given rational numbers, option A is incorrect.

Considering option B,

Since the three numbers are recurring and terminating rational numbers and \[0.7\] does not lie between the two given rational numbers, option B is also incorrect.

Considering option C,

All the three irrational numbers \[0.75075007500075000075...\], \[0.7670767007670007670000767...\], \[0.808008000800008...\] lies between the given rational number.

Hence, option C is correct.

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