## Real Numbers – Revisiting Rational and Their Decimal Expansions

REVISITING RATIONAL NUMBERS AND THEIR DECIMAL EXPANSIONS : We have already studied in the previous class that rational numbers have either a terminating decimal repeating decimal expansion. We have to consider a rational number as (where ) as terminating or non-terminating repeating (or recurring) decimal expansion. e.g.     (A)    (i)    0.0527    =         (ii)    26.12489     =      (B)    (i)    0.0875    =         (ii)    23.3408    =     Now, we […]

## Real Number-Revisiting Irrational Numbers

REVISITING IRRATIONAL NUMBERS : We have studied in the previous class about rational numbers as well as irrational numbers. Both are the members of the REAL NUMBERS family. We have also studied how to locate irrational numbers on the number line. Any rational number is represented by ; where whereas irrational number is represented by […]

## Real Numbers-The Fundamental Theorem of Arithmetic

THE FUNDAMENTAL THEOREM OF ARITHMETIC We have already studied in the previous classes that any natural can be written as a product of its prime factors. e.g. = 3 = 3, 6 = 2 3, 275 = 11 25 etc. i.e, any natural number can be obtained by multiplying prime numbers. If we take prime […]

## Real Numbers: Euclid’s Division Lemma

EUCLID’S DIVISION LEMMA : Euclid was the first Greek Mathematician who gave a new way of thinking the study of geometry. He also made important contributions to the number theory. Euclid’s Lemma is one of them. It is a proven statement which is used to prove other statements. Let ‘a’ and ‘b’ be any two […]

## Class 10th Mathematics – Real Numbers

Real Numbers Introduction Euclid’s Division Lemma The Fundamental Theorem of Arithmetic Revisiting Irrational Numbers Revisiting Rational Numbers and Their Decimal Expansions Summary INTRODUCTION : We have already studied about irrational numbers in 9th class. Now, we will study the real numbers and also about the important properties of positive integers for Euclid’s division algorithm and […]