Question

Write whether the following rational numbers will have a terminating or a non terminating decimal expansion
1) 51/1500
2) 189/125
3)29/ 2 SQUARE ×5×7
3) 6/200
4) 141/120
CAN ANYBODY OUT THERE EXPLAIN IT TO ME.....
I HAVE EXAM TOMORROW ...PLZZZZZ

Answer 1

1) 51/1500 is a terminating decimal as it has the quotient 0.032 which is not repeated.
2)189/125 is terminating decimal with quotient 1.512
3)6/200 is terminating decimal with quotient 0.03
4)141/120 is terminating decimal with quotient 1.175

A decimal is Known as terminating when the quotient is repeated.

Answer 2

1)51/1500
51/5^3×2^3+500
therefore non terminating
2)189/125
189/5^3
therefore terminating
3)29/2^2×5×7
29/4×35
29/140
29/5^3+5^2
therefore. non terminating
4)6/200
6/5^2×2^3
therefore terminating
5)141/120
141/24×5
141/5×2^3×3
therefore non terminating