Q1 of 104 Page 1

Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.

Given rational number is


is terminating if


a) p and q are co-prime &


b) q is of the form of 2n 5m where n and m are non-negative integers.


Firstly, we check co-prime


13 = 13 × 1


125 = 5 × 5 × 5


13 and 125 have no common factors


Therefore, 13 and 125 are co-prime.


Now, we have to check that q is in the form of 2n5m


125 = 53


= 1 × 23


= 20 × 53


So, denominator is of the form 2n5m where n = 0 and m = 3


Thus, is a terminating decimal.


More from this chapter

All 104 →
1

Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.

 1

Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.

 1

Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.

 1

Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.