A rational number in its decimal expansion is 1.7112 what can you say about the prime factor of q. When this number is expressed in the form of p/q ?
Answers
Answered by
39
Hi ,
Let x = 1.7112
x = 17112/ 10000 = p/q
q = 10000
q = ( 10 )⁴
q = ( 2 × 5 )⁴
q = 2⁴ × 5⁴ = 2^n × 5^m
******************************************
Let x = p/q be a rational number,
such that the prime factorization of
q is of the form 2^n × 5^m , where
n and m are non - negative integers.
Then x has a decimal expansion
which terminates.
I hope this helps you.
: )
Let x = 1.7112
x = 17112/ 10000 = p/q
q = 10000
q = ( 10 )⁴
q = ( 2 × 5 )⁴
q = 2⁴ × 5⁴ = 2^n × 5^m
******************************************
Let x = p/q be a rational number,
such that the prime factorization of
q is of the form 2^n × 5^m , where
n and m are non - negative integers.
Then x has a decimal expansion
which terminates.
I hope this helps you.
: )
Answered by
5
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this number is expressed in the form of p/q ?
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