Write down the decimal expansion of 13/64 without actual division
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Hi ,
Let x = p / q be a rational number such
that the prime factorisazation of ' q ' is
of the form 2^n × 5^m , where n , m are
non- negative integers .Then ' x ' has a
decimal expansion which terminates.
Here,
x = p/q = 13/64
q = 64
q = 2 × 2 × 2 × 2 × 2 × 2
q = 2^6
13/64 = 13/2^6
= ( 13 × 5^6 )/( 2^6 × 5^6 )
= ( 13 × 15625 )/ (2^6 × 5^6)
= 203125/(2^6 × 5^6 )
Therefore,
q = 2^6 × 5^6 for n= 6, m= 6 , so
13 /64 = 0.203125 is a terminating decimal
I hope this helps you.
:)
Let x = p / q be a rational number such
that the prime factorisazation of ' q ' is
of the form 2^n × 5^m , where n , m are
non- negative integers .Then ' x ' has a
decimal expansion which terminates.
Here,
x = p/q = 13/64
q = 64
q = 2 × 2 × 2 × 2 × 2 × 2
q = 2^6
13/64 = 13/2^6
= ( 13 × 5^6 )/( 2^6 × 5^6 )
= ( 13 × 15625 )/ (2^6 × 5^6)
= 203125/(2^6 × 5^6 )
Therefore,
q = 2^6 × 5^6 for n= 6, m= 6 , so
13 /64 = 0.203125 is a terminating decimal
I hope this helps you.
:)
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