Question

without actually calculating by long division state whether the following rational numbers have a terminating decimal expansion or non-terminating repeating decimal expansion for 1)27/40 2)7/20​

Answer 1

q1  27/40

  =  27/$2^{3}$x5      q=$2^{n}$x$5^{m}$

 =27x$5^{2}$/$2^{3}$x$5^{3}$

=27x25/$10^{3}$

=675/1000

=0.675

q2  7/20

=7/$2^{2}$x5

=7x5/$2^{2}$x5x5

=35/$2^{2}$x$5^{2}$

=35/$10^{2}$

=35/100

=0.35

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