Question

Without actual division state whether thr following number will have a terminating or non-terminating decimal expansion.
a.158/2^2×5^2×13
b.123/120​

Answer 1

Answer:

(i) The given number is 23/8

Here, 8 = 23 and 2 is not a factor of 23.

So, the given number is in its simplest form.

Now, 8 = 23 is of the form 2m × 5n, where m = 3 and n = 0.

So, the given number has a terminating decimal expansion.

(ii) The given number is 125/441

Here, 441 = 32 × 72 and none of 3 and 7 is a factor of 125.

So, the given number is in its simplest form.

Now, 441 = 32 × 72 is not of the form 2m × 5n

So, the given number has a non-terminating repeating decimal expansion.

(iii) The given number is 35/50 and HCF (35, 50) = 5.

Here, 7/10 is in its simplest form.

Now, 10 = 2 × 5 is of the form 2m × 5n, where in = 1 and n = 1.

So, the given number has a terminating decimal expansion.

(iv) The given number is 77/210 and HCF (77, 210) = 7.

Here, 11/30 is in its simplest form. 30

Now, 30 = 2 × 3 × 5 is not of the form 2m × 5n.

So, the given number has a non-terminating repeating decimal expansion.

(v) The given number isClearly, none of 2, 5 and 7 is a factor of 129.

So, the given number is in its simplest form.

Step-by-step explanation:

plz gave me brainlist Mark☺☺☺☺☺

Answer 2

(i) The given number is 23/8

Here, 8 = 23 and 2 is not a factor of 23.

So, the given number is in its simplest form.

Now, 8 = 23 is of the form 2m x 5n, where m

= 3 and n = 0.

So, the given number has a terminating decimal expansion.

(ii) The given number is 125/441

Here, 441 = 32 x 72 and none of 3 and 7 is a

factor of 125.

So, the given number is in its simplest form.

Now, 441 = 32 x 72 is not of the form 2m x 5n

So, the given number has a non-terminating repeating decimal expansion.

(iii) The given number is 35/50 and HCF (35,

50) = 5.

84

Here, 7/10 is in its simplest form.

Now, 10 = 2 × 5 is of the form 2m x 5n, where

in = 1 and n = 1.

So, the given number has a terminating decimal expansion.

(iv) The given number is 77/210 and HCF (77, 210) = 7.

Here, 11/30 is in its simplest form. 30

Now, 30 = 2 3 x 5 is not of the form 2m x

5n.

So, the given number has a non-terminating repeating decimal expansion.

(v) The given number isClearly, none of 2,5 and 7 is a factor of 129.

So, the given number is in its simplest form.