show that 19/2³5^6 will have terminating decimal expression.
Answers
Answered by
15
Hii friend,
we know that any real number which have Denominator in the form 2^m 5^n where m and n are positive integer , will always terminating decimal , Since in the given case Denominator is 2^3 5^6 .
19/2^3 5^6 is terminating decimal..
HOPE IT WILL HELP YOU...... :-)
we know that any real number which have Denominator in the form 2^m 5^n where m and n are positive integer , will always terminating decimal , Since in the given case Denominator is 2^3 5^6 .
19/2^3 5^6 is terminating decimal..
HOPE IT WILL HELP YOU...... :-)
Answered by
3
Hi ,
19/( 2³ × 5^6 ) = p/q
q = 2³ × 5^6
Now , q is in the form of 2^n× 5^m,
Where n , m are positive integers.
Therefore ,
19/ ( 2³ × 5^6 ) is a terminating
decimal.
19/ ( 2³ × 5^6 )
= ( 19 × 2³ ) / ( 2³ × 2³ × 5^6 )
= ( 19 × 8 ) / ( ( 2 × 5 )^6
= 152/ ( 10 )^6
= 0.000152 ( terminating decimal )
I hope this helps you.
: )
19/( 2³ × 5^6 ) = p/q
q = 2³ × 5^6
Now , q is in the form of 2^n× 5^m,
Where n , m are positive integers.
Therefore ,
19/ ( 2³ × 5^6 ) is a terminating
decimal.
19/ ( 2³ × 5^6 )
= ( 19 × 2³ ) / ( 2³ × 2³ × 5^6 )
= ( 19 × 8 ) / ( ( 2 × 5 )^6
= 152/ ( 10 )^6
= 0.000152 ( terminating decimal )
I hope this helps you.
: )
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