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The decimal expansion of 987/10500 will terminate after
- a)3 decimal places
- b)2 decimal places
- c)1 decimal place
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The decimal expansion of987/10500will terminate aftera)3 decimal place...
987 = 3 x 7 x 47
10500 = 2 x 2 x 3 x 5 x 5 x 5 x 7
HCF of 987 and 10500 = 3 x 7 = 21
Therefore ,
Least form of the fraction = 987 / 10500
Divide numerator and denominator with HCF,
we get,
= ( 987 / 21 ) / ( 10500 / 21 )
= 47 / 500
987 / 10500 = 47 / 500
Denominator = 500
= 2^2 x 5^2
We have only 2 and 5 as factors .
Therefore ,
987 / 10500 is terminating decimal.
as 47/500 = 0.094 so The decimal expansion of 987/10500 will terminate after 3 decimal places
Most Upvoted Answer
The decimal expansion of987/10500will terminate aftera)3 decimal place...
Decimal Expansion of 987/10500
To determine whether the decimal expansion of 987/10500 terminates or not, we need to express the given fraction in its simplest form.
First, let's find the greatest common divisor (GCD) of the numerator (987) and the denominator (10500). The GCD of 987 and 10500 is 3.
Now, we divide both the numerator and denominator by their GCD to simplify the fraction:
987 ÷ 3 = 329
10500 ÷ 3 = 3500
So, the simplified fraction is 329/3500.
Terminating Decimal or Non-Terminating Decimal
To determine whether a decimal expansion terminates or not, we need to consider the prime factors of the denominator.
The prime factorization of the denominator 3500 is:
3500 = 2^2 × 5^3 × 7
A decimal expansion terminates if and only if the denominator of the fraction has only the prime factors 2 and/or 5.
Since the prime factorization of 3500 includes the prime factor 7, the decimal expansion of 987/10500 will not terminate.
Conclusion
Therefore, the correct answer is option 'D' - None of these. The decimal expansion of 987/10500 will not terminate.
To determine whether the decimal expansion of 987/10500 terminates or not, we need to express the given fraction in its simplest form.
First, let's find the greatest common divisor (GCD) of the numerator (987) and the denominator (10500). The GCD of 987 and 10500 is 3.
Now, we divide both the numerator and denominator by their GCD to simplify the fraction:
987 ÷ 3 = 329
10500 ÷ 3 = 3500
So, the simplified fraction is 329/3500.
Terminating Decimal or Non-Terminating Decimal
To determine whether a decimal expansion terminates or not, we need to consider the prime factors of the denominator.
The prime factorization of the denominator 3500 is:
3500 = 2^2 × 5^3 × 7
A decimal expansion terminates if and only if the denominator of the fraction has only the prime factors 2 and/or 5.
Since the prime factorization of 3500 includes the prime factor 7, the decimal expansion of 987/10500 will not terminate.
Conclusion
Therefore, the correct answer is option 'D' - None of these. The decimal expansion of 987/10500 will not terminate.
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Community Answer
The decimal expansion of987/10500will terminate aftera)3 decimal place...
After 3 decimal places
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The decimal expansion of987/10500will terminate aftera)3 decimal placesb)2 decimal placesc)1 decimal placed)None of theseCorrect answer is option 'A'. Can you explain this answer?
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