Question

which one of the following rational number will have terminating decimal

1) 5/48 2)2/23. 3)3/75 4)7/27

Answer 1

Hey there !!


→ The answer of your question is option 3 = 3/75 .


▶ Explanation:-

→ Terminating decimal expansion :- If prime factor of denominator of a rational number is only 2 or 5 or both then its decimal expansion will be terminating.

→ Non - terminating decimal expansion :- If denominator of a rational number is a prime factor other than 2 or 5 then its decimal expansion will be non terminating.



1. 5/48 .

Denominator = 48 = 2 × 2 × 2 × 2 × 3 .

Have factor other than 2 or 5 , so 5/48 is non- terminating decimal expansion.


2. 2/23 .

Denominator = 23 = 1 × 23 .

Have factor other than 2 or 5 , so 5/48 is non- terminating decimal expansion.


3. 3/75 = 1/25 .

Denominator = 25 = 5 × 5 .

Have only 5, so it is a Terminating decimal.


4. 7/27 .

Denominator = 27 = 3 × 9 .

Have factor other than 2 or 5 , so 5/48 is non- terminating decimal expansion.


✔✔ Hence, it is solved ✅✅.

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THANKS



#BeBrainly.

Answer 2

national number will have terminating decimal when its denominator have a factor of 2 or 5 both,

3) 3/75✔️✔️

Now,

1. 5/48
48=2×2×2×2×3❌

2. 2/23
23=1×24❌

3. 3/75=1/25
25=5×5✔️

4. 7/27
27=3×9❌