Exercise 1A Solution - Number System

Number System is a fundamental concept in mathematics that deals with the representation of numbers in various forms. It is essential to understand the different types of number systems to perform mathematical operations accurately. Let's discuss the solutions for Exercise 1A related to the Number System.

Question 1: Write the rational number between √2 and √3.

Solution: To find the rational number between √2 and √3, we need to take their average. The average of two numbers is always a rational number.

Hence, the rational number between √2 and √3 is (√2 + √3)/2.

Question 2: Find two irrational numbers between 0.1 and 0.15.

Solution: To find the irrational numbers between 0.1 and 0.15, we need to consider their decimal expansions. We can write 0.1 as 0.1000000.... and 0.15 as 0.1500000.....

Hence, two irrational numbers between 0.1 and 0.15 are:

- 0.11323232323.... (irrational because it does not repeat or terminate)
- 0.142857142857.... (irrational because it is a non-repeating and non-terminating decimal)

Question 3: Find the smallest rational number and the smallest irrational number between 1/√5 and 2/√5.

Solution: To find the smallest rational number between 1/√5 and 2/√5, we need to take their average. The average of two rational numbers is always a rational number.

Hence, the smallest rational number between 1/√5 and 2/√5 is (1/√5 + 2/√5)/2 = (√5/5 + 2√5/5)/2 = 3√5/10.

To find the smallest irrational number between 1/√5 and 2/√5, we need to take the square root of the smallest rational number. Hence, the smallest irrational number is √(3√5/10).

In summary, Exercise 1A related to the Number System helps us understand the concept of rational and irrational numbers and how to find them between two given numbers. It is essential to practice such exercises to strengthen our mathematical skills.

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