1) 0.125 = 125/1000 = 125/10

3) 0.7 = 7/10 = 7/(2 x 5)

2) Theorem 2 : Let x = p/q be a rational number, such that the prime factorization of q is of the form 2

3) Let x =p/q be a rational number, such that the prime factorization of q is not of the form 2

Examples :

1) State whether the following rational numbers will have terminating decimal-expansion or a non-terminating repeating expansion of decimal.

a) 17/8

17/8 = 17/(2

As the denominator is of the form 2

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b) 64/255

64/255 = 64/ (5 x 3 x 17)

Clearly, 255 is not of the form 2

• Euclid Geometry

• Euclids division lemma

• Euclids division Algorithm

• Fundamental Theorem of Arithmetic

• Finding HCF LCM of positive integers

• Proving Irrationality of Numbers

• Decimal expansion of Rational numbers

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