Question

without actually performing the long division state whether the following rational numbers are terminating or non terminating decimal expansion 13/250​

Answer 1

Answer:

terminating number's denominator is only in the form 2^n*5^m where m and n are real number

∴(1) 19/250=19/(2^1*5^3)

where m=3 and n=1

hence terminating (2) 23/2048=23/(2^11*5^0)

where m=0 and n=11

hence terminating(3) 127/910=127/(2^1*5^1*7^1)

where m=1 and n=1 having factor 7

hence non-terminating(4) 54/434=54/(2^1*5^0*7^1*13^1)

where m=0 and n=1 having factor 7 and 13 hence non-terminating(5) 52/(2^3*5^4) where m=4 and n=3 hence terminating.

Answer 2

Answer:

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