7. Without actual division, determine that 51/90
has a terminating decimal representation or not
Answers
The rational not having denominator as multiple of 2m×5n will be non terminating.
(1) 167=2×2×2×27− denominator is multiple of 2m×5n hence terminating.
(2) 12523=5×5×523 -- denominator is multiple of 2m×5n hence terminating.
(3) 149=7×29 -- denominator is not multiple of 2m×5n hence non-terminating
(4)4532=3×3×532-- denominator is not multiple of 2m×5n hence non-terminating.
(5) 5043=5×5×243-- denominator is multiple of 2m×5n hence terminating.
(6)4017=2×2×2×517 -- denominator is multiple of 2
Step-by-step explanation:
Given :-
51/90
To find :-
Without actual division, determine that 51/90 is a terminating decimal representation or not ?
Solution :-
Given rational number = 51/90
=> (3×17)/(3×30)
On cancelling 3 in both the numerator and the denominator then
=> 17/30
30 = 2×3×5
17/30 can be written as
=> 17/(2×3×5)
The denominator = 2×3×5
It is not in the form of 2^m × 5^n
So , it is not a terminating decimal.
Answer :-
51/90 is not a terminating decimal.
Check :-
51/90 = 17/30
30) 170 ( 0.5666...
150
_______
200
180
_________
200
180
_________
200
180
_________
20
___________
51/90 = 0.56666...
It is not a terminating decimal.
It is a non terminating recurring decimal.
Used formulae:-
→ x = p/q is a rational number, if q is in the form of 2^m × 5^n then x is a terminating decimal.