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RD Chapter 1 Number Systems Ex 1.4 Solutions

Question - 1 : - Define an irrational number.

Answer - 1 : - A number which cannot be expressed in the form of pq where p and q are integers and q ≠ 0 is called an irrational number.

Question - 2 : - Explain, how irrational numbers differ from rational numbers?

Answer - 2 : - A rational number can be expressed in either terminating decimal or non-terminating recurring decimals but an irrational number is expressed in non-terminating non-recurring decimals.

Question - 3 : - Examine, whether the following numbers are rational or irrational:

Answer - 3 : -


Question - 4 : - Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:

Answer - 4 : -


Question - 5 : - In  the following equation, find which variables x, y, z etc. represent rational or irrational numbers:

Answer - 5 : -


Question - 6 : - Given two rational numbers lying between 0.232332333233332… and 0.212112111211112.

Answer - 6 : - Two rational numbers lying between 0.232332333233332… and 0.212112111211112… will be 0.232 and 0.212

Question - 7 : - Give two rational numbers lying between 0.515115111511115… and 0.5353353335…

Answer - 7 : - Two rational numbers lying between 0.515115111511115… and 0.535335333533335… will be 0.515, 0.535

Question - 8 : - Find one irrational numbers between 0.2101 and 0.2222… =

Answer - 8 : - One irrational number lying between 0.2101 and 0.2222… =  will be 2201.0010001…


Question - 9 : -
Find a rational number and also an irrational number lying between the numbers, 0.3030030003… and 0.3010010001…

Answer - 9 : -

Between two numbers 0.3030030003… and 0.3010010001…, a rational will be 0.301 and irrational number will be 0.3020020002…

Question - 10 : - Find three different irrational numbers between the rational numbers 

Answer - 10 : -


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