Chapter 1 of CBSE NCERT Class 9 Math covers number systems. Concepts covered in chapter 1 include rational numbers, irrational numbers, rationalizing irrational numbers by multiplying with their conjugates, decimal expansion of real numbers, operations on real numbers and laws of exponents or rules of indices. The extra questions given below include questions akin to HOTS (Higher Order Thinking Skills) questions and exemplar questions of NCERT.
Here is a quick recap of the key concepts that are covered in this chapter in the CBSE NCERT Class 9 Math text book.
A number that can be written in the form
Possibility 1: If the decimal expansion of the number is terminating it is a rational number. Note: Integers are terminating decimals and are therefore, rational numbers.
Possibility 2: If the decimal expansion of the number is non-terminating but is recurring, it is rational. Example
A number that CANNOT be written in the form
If the decimal expansion of the number is non-terminating AND non-recurring it is an irrational number. Example:
For an irrational number of the form a + √b, a - √b is its conjugate. And for an irrational number of the from a - √b, a + √b is its conjugate.
To rationalize the denominator of
i.e., multiply and divide
If a > 0 is a real number and m and n are rational numbers, the following laws of exponents hold good.
Prime Factorise & Rationalise Denominator:
Rational numbers - Fractions:
Find 5 rational numbers between
Express as Fractions
Express 1.363636... in the form
Express in the form
Express 0.4323232… in the form
Simplify the following
(a)
(b)
(c)
Rationalize the denominator:
(a)
(b)
(c)
(d)
Simplify and find the value of
(a) (729)
(b) (64)
(c) (243)
(d) (21)
(e)
Operation on real numbers & Algebraic identities
If x =
Rationalise & find value of cubic expression
If x =
Rationalise the denominator
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