Question

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

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

Answer:

Part A

Rational number : The numbers which can be written in the form of p/q are known as rational numbers

5.4 = 54/10 = 27/5 (It can be written in the form of p/q)

The rational number between 5.2 and 5.5 is 5.4

Part B

Irrational number : The numbers which cannot be written in the form of p/q are known irrational numbers

The irrational number between 5.2 and 5.5 is √29 whose value is 5.385164807134

On rounding off to nearest hundredth we get 5.385

The irrational number between 5.2 and 5.5 is 5.385

HOPE IT HELPS YOU

Step-by-step explanation:

Answer 2

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

Learn More:

Decimal expansion of a rational number Fill in the blanks hair ...

brainly.in/question/10914508

1. The decimal expansion of27/15000 terminate afterhow many ...

brainly.in/question/18225164