Without actually performing the long division state whether the following rational number will have a terminating decimal expansion or not. Also, write the terminating decimal expansion, if exists.
i) 3/8
ii) 14588/625
iii) 31/ 343
iv) 51/1500
Answers
Answered by
43
Heya!
Here is yr answer.....
Terminating decimal :
~~~~~~~~~~~~~~~~~~~
If the denominator of the no. can be written in the form of 2^n × 5^m ...then It is terminating decimal!
Coming to yr ques -----
(i) 3/8
=> 3/2³×5^0
It is terminating decimal!
=> 3×5³/2³×5³
=> 3×125/(10)³
=> 375/100
=> 0.375
(ii) 14588/625
=> 14588/5^4×2^0
It is terminating decimal!
=> 14588×2^4/5^4×2^4
=> 14588×16/(10)^4
=> 233408/10000
=> 23.3408
(iii) 31/343
=> 31/7³
Since, denominator is not in the form of 2^n × 5^m .It is non-terminating decimal!
(iv) 51/1500
=> 51/2²×5³×3¹
it is in the form of 2^n × 5^m .But, there 3¹ is also present. So, it is non-terminating reccuring decimal!
Hope it hlpz...
Here is yr answer.....
Terminating decimal :
~~~~~~~~~~~~~~~~~~~
If the denominator of the no. can be written in the form of 2^n × 5^m ...then It is terminating decimal!
Coming to yr ques -----
(i) 3/8
=> 3/2³×5^0
It is terminating decimal!
=> 3×5³/2³×5³
=> 3×125/(10)³
=> 375/100
=> 0.375
(ii) 14588/625
=> 14588/5^4×2^0
It is terminating decimal!
=> 14588×2^4/5^4×2^4
=> 14588×16/(10)^4
=> 233408/10000
=> 23.3408
(iii) 31/343
=> 31/7³
Since, denominator is not in the form of 2^n × 5^m .It is non-terminating decimal!
(iv) 51/1500
=> 51/2²×5³×3¹
it is in the form of 2^n × 5^m .But, there 3¹ is also present. So, it is non-terminating reccuring decimal!
Hope it hlpz...
Answered by
0
Answer:
non-terminating decimal.
Step-by-step explanation:
hope uh like my answer
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