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NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
CBSE
Textbook
NCERT
Class
Class 10
Subject
Maths
Chapter
Chapter 1
Chapter Name
Real Numbers
Exercise
Ex 1.1, Ex 1.2, Ex 1.3, Ex 1.4
Number of Questions Solved
18
Category
NCERT Solutions
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Board
NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers
Real Numbers CBSE Class 10 Maths Chapter 1 Solutions
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1.1 Introduction
1.2 Euclid’s Division Lemma
1.3 The Fundamental Theorem Of Arithmetic
1.4 Revisiting Irrational Numbers
1.5 Revisiting Rational Numbers And Their Decimal Expansions
1.6 Summary
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions For Class 10 Maths Real Numbers Exercise 1.1
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Formulae Handbook for Class 10 Maths and Science
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NCERT Solutions
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 10 Social
NCERT Solutions for Class 10 English
NCERT Solutions for Class 10 Hindi
NCERT Solutions for Class 10 Sanskrit
NCERT Solutions for Class 10 Foundation of IT
RD Sharma Class 10 Solutions
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
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NCERT Solutions For Class 10 Maths Real Numbers Exercise 1.2
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
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NCERT Solutions For Class 10 Maths Real Numbers Exercise 1.3
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
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NCERT Solutions For Class 10 Maths Real Numbers Exercise 1.4
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
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NCERT Solutions for Class 10 Maths
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Real Numbers:
Rational numbers and irrational numbers taken together form the set of real numbers. The set
of real numbers is denoted by R. Thus every real number is either a rational number or an
irrational number. In either case, it has a non–terminating decimal representation. In case of
rational numbers, the decimal representation is repeating (including repeating zeroes) and if
the decimal representation is non–repeating, it is an irrational number. For every real number,
there corresponds a unique point on the number line ‘l’ or we may say that every point on the
line ‘l’ corresponds to a real number (rational or irrational).
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From the above discussion we may conclude that:
To every real number there corresponds a unique point on the number line and conversely, to
every point on the number line there corresponds a real number. Thus we see that there is
one–to–one correspondence between the real numbers and points on the number line ‘l’, that
is why the number line is called the ‘real number line’.
Objectives:
The students will be able to ;
prove Euclid's Division Lemma
state fundamental theorem of arithmetic
find HCF and LCM using prime factorisation
establish the given number as an irrational number
conclude the decimal expansion of a rational number is either terminating or non-terminating
repeating.
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 10 Maths
Summary:
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We have studied the following points:
1. Euclid’s Division Lemma : Given positive integers a and b, there exist whole numbers q
and r satisfying a = bq + r where 0 = r = b.
2. Euclid’s Division Algorithm: According to this, which is based on Euclid’s division
lemma, the HCF of any two positive integers a and b with a > b is obtained as follows:
Step 1 Apply the division lemma to find q and r where a = bq + r, O = r < b.
Step 2 If r = 0, the HCF is b . If r ? 0 apply Euclid Lemma to b and r
Step 3 Continue the process till the remainder is zero. The divisor at this stage will be HCF
(a, b). Also HCF (a, b) = HCF (b, r)
3. The Fundamental Theorem of Arithmetic: Every composite number can be expressed
(factorised) as a product of primes and this factorisation is unique, apart from the order in
which the prime factors occur.
NCERT Solutions for Class 10 Maths
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