without actual division determine whether the decimal expansion of the rational no 51/84 is terminating or non terminating recurring
Answers
Answer:
Answer
We know that
q
p
is terminating if p and q are co-prime and q is of the form 2
m
5
n
; where m and n are non-negative integers.
(A)
25
3
:
Checking co-prime-
Since 3 and 25 have no common factors, hence 3 and 25 are co-prime.
Now,
25=5×5=5
2
∴ Denominator=5
2
=1×5
2
=2
0
×5
2
∴ Denominator is of the form 2
m
5
n
, where m = 0 and n = 2.
Hence,
25
3
is a terminating decimal.
(B)
18
11
:
Checking co-prime-
Since 11 and 18 have no common factors, hence 11 and 18 are co-prime.
Now,
18=2×3×3=2×3
2
∴ Denominator is not of the form 2
m
5
n
.
Hence,
18
11
is not a terminating decimal.
(C)
20
13
:
Checking co-prime-
Since 13 and 20 have no common factors, hence 13 and 20 are co-prime.
Now,
20=2×2×5=2
2
×5
∴ Denominator=2
2
×5=2
2
×5
1
∴ Denominator is of the form 2
m
5
n
, where m = 2 and n = 1.
Hence,
20
13
is a terminating decimal.
(D)
42
41
:
Checking co-prime-
Since 41 and 42 have no common factors, hence 41 and 42 are co-prime.
Now,
42=2×3×7
∴ Denominator is not of the form 2
m
5
n
.
Hence,
42
41
is not a terminating decimal.
Answer:
thnx for the ans vro huehuehuehue