Question

Which of the following rational numbers have terminating decimal?
(i) 16/225 (ii) 5/18
(iii) 2/21 (iv) 7/250
A. (i) and (ii)
B. (ii) and (iii)
C. (i) and (iii)
D. (i) and (iv)

Answer 1

(i) Given :   16/125

16/2° × 5³

Here, the factors of the denominator 125 are 2° × 5³ which is in the form 2^m 5ⁿ .

So , 13/125 has a terminating decimal .

(ii)  

5/18

5/2¹× 3²

Here, the factors of the denominator 18 are 2¹ × 3² which is not in the form 2^m 5ⁿ .

So , 5/18 has a non terminating decimal.

(iii)  

2/21

2/3¹× 7¹

Here, the factors of the denominator 21 are 3¹ × 7¹ which is not in the form 2^m 5ⁿ .

So , 2/21 has a non terminating decimal.

(iv)

7/250

7/ 2¹ × 5³  

Here, the factors of the denominator 250 are 2¹ × 5³ which is in the form 2^m 5ⁿ .

So , 7/250 has a non terminating decimal.

Hence, rational numbers 16/125 & 7/250 have terminating decimals.

Among the given options option (D) (i) and (iv) are correct .

HOPE THIS ANSWER WILL HELP YOU…

 

Some more questions :  

Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

(i) $\frac{23}{8}$

(ii) $\frac{125}{441}$

(iii) $\frac{35}{50} [NCERT]$

(iv) $\frac{77}{210} [NCERT]$

(v) $\frac{129}{2^{2} * 5^{7} * 7^{17}}$

(vi) $\frac{987}{10500}$

https://brainly.in/question/6751559

 

Write down the decimal expansions of the following rational numbers by writing their denominators in the form $2^{m} * 5^{n}$, where,m,n are non-negative integers.

(i) $\frac{3}{8}$

(ii) $\frac{13}{125}$

(iii) $\frac{7}{80}$

(iv) $\frac{14588}{625}$

(v) $\frac{129}{2^{2} * 5^{7}}$ [NCERT]

https://brainly.in/question/6760419

Answer 2

Step-by-step explanation:

HEY THERE!!!

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As we know that a number terminates when it is in the form P/ Q

where Q can be written in form 2^m × 5^n .

So according to this , option D) 7 / 250 is the correct answer.

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Hope this helps!!!!