Euclid’s Division Lemma Composite number The Fundamental Theorem of Arithmetic chapter 1 can study by students of class 10. These definitiona and formulas of Class 10 Maths Chapter 1: Real Numbers is developed and witten by our expert teachers. Maths formulas. Euclid’s Division Lemma Composite number The Fundamental Theorem of Arithmetic Theorem of rational number Theorem of terminator Theorem of non-terminating repeating (recurring) is prepapred and collected from varius resources to help the students.
for any prime number p which is divides a^2 then it will divide a also.
For example: 5 divides 100 then it will divide root of 100( 10) also.
for any rational number x which is written as p/q and if q can be written in form of 2^n*p^m and value of m and n are positive integer or equal to 0 then decimal expansion of x will terminate.
For example take x = 7/50
And 50 = 2*5*5 = 2^1*5^2
And powers 1 and 2 both are positive integer So value of x will terminate
for any rational number x which is written as p/q and if q can’t be written in form of 2^n*p^m and value of m and n are positive integer or equal to 0 then decimal expansion of x will non-terminating repeating (recurring).
For example
X = 7/15
Here denominator 15 = 3*5
And it cannot be written in form of 2^n*5^m
x =0.4666……………
So x will non-terminating repeating (recurring) .
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