Question

identify 51by 64have terminating or non terminating decimal expansion without division​

Answer 1

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.