Question

Part A: Find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points)

Part B: Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth

Answer 1

Given :  Numbers 5.2 and 5.5

To Find : Rational number in between

An irrational number in between and then approximate to nearest hundredth

Solution:

Rational numbers are real numbers which can be written in the form p/q where p and q are integers and q≠0

All real numbers which are not rational  are irrationals.

Note: There exist Infinite rational / irrational numbers between any two different rational / irrational numbers.

Numbers 5.2 and 5.5

5.3 , 5.4  are two examples of  rational number between 5.2 and 5.5

5.3 = 53/10  is p/q form where p and q are integers and q ≠ 0.

Hence Rational

5.4 = 54/10 = 27/5  is p/q form where p and q are integers and q ≠ 0.

Hence Rational

Let say  x represent irrational number between 5.2 and 5.5

5.2  < x  < 5,5

=> (52/10)  <  x < 55/10

=> 52²/100 < x²  < 55²/100

=> 2704/100 < x² < 3025

x²= 3000/100       ( x² can take any integer or non integer value between 2704/100 and 3025/100 except 53²/100 =2809/100   and  54² = 1916/100)

x= √30   is an irrational number between

x  ≈ 5.48

Another example can be

x= √29

x  ≈ 5.39

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