Chapter no.1 Real Numbers ( Exercise 1.4)
Today we are going to learn the Rational numbers and Their decimal expansions from chapter 1 of your Mathematics textbook .
Rational numbers :- Rational number is a number, which can be expressed in the form of p/q , where p and q are integers and q not equal to zero.
e.g 2/3 , -4 , -5/2 etc.
Decimal Expansion of Rational numbers :-
The decimal expansion of rational numbers are of two types i.e. Terminating decimal expansion and Non-terminating repeating (recurring) decimal expansion.
1) Let x = p/q be a rational number, such that the prime factorisation of q is of the form of 2 to the power n 5 to the power m , where m & n are non-negative integers. Then x has a decimal expansion which terminates.
2) Let x = p/q be a rational number, such that the prime factorisation of q is not of the form 2 to the power n 5 to the power m , where m & n are non-negative integers. Then x has a decimal expansion which is Non-terminating repeating ( recurring ).
Now observe the examples
Today we are going to learn the Rational numbers and Their decimal expansions from chapter 1 of your Mathematics textbook .
Rational numbers :- Rational number is a number, which can be expressed in the form of p/q , where p and q are integers and q not equal to zero.
e.g 2/3 , -4 , -5/2 etc.
Decimal Expansion of Rational numbers :-
The decimal expansion of rational numbers are of two types i.e. Terminating decimal expansion and Non-terminating repeating (recurring) decimal expansion.
1) Let x = p/q be a rational number, such that the prime factorisation of q is of the form of 2 to the power n 5 to the power m , where m & n are non-negative integers. Then x has a decimal expansion which terminates.
2) Let x = p/q be a rational number, such that the prime factorisation of q is not of the form 2 to the power n 5 to the power m , where m & n are non-negative integers. Then x has a decimal expansion which is Non-terminating repeating ( recurring ).
Now observe the examples
Remaining questions of Exercise 1.4
The video of solutions of exercise 1.4 are available in following link
Homework :- Solve Exercise 1.4
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