Question

state whether the following numbers 1)13/3125 ,2)27/1500 will have a terminating decimal expansion or a non terminating repeating decimal

Answer 1

If the denominator is in the form of 2^n*5^m then the number can be represented by terminating decimal.
i)13/3125

3125= 5^5
Denominator 3125 =2^0*5^5
13/3125 = 13/5^5

=(13*2^5)/(5^5*2^5)
=(13*32)/(10)^5
=416/100000
=0.00416(terminating decimal)
2)27/1500
=(3*9)/(3*5*5*5*2*2)
=9/(5*5*5*5*2*2)
=(9*2)/(5*5*5*2*2*2)
=18/1000
=0.018(terminating decimal)

Answer 2

You answer would be 0.018