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Which of the following decimal number is a rational number with denominator 37?
- a)0.459459459⋯
- b)0.459459459
- c)0.0459459459⋯
- d)0.00459459459⋯
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Which of the following decimal number is a rational number with denomi...
459 = 17 × 27
Second option is terminating decimal, ∴ denominator has a prime factors of 2 or 5 only
Second option is terminating decimal, ∴ denominator has a prime factors of 2 or 5 only
We can evaluate the first decimal and other two decimals are obtained by dividing it by 10 and 100 respectively
Let x = 0.459459459⋯
1000x = 459.459459⋯
1000x = 459 + 0.459459⋯
1000x = 459 + x
∴ 999x = 459
x = 459/999 = (17 × 27) / (37 × 27) = 17/37
1000x = 459.459459⋯
1000x = 459 + 0.459459⋯
1000x = 459 + x
∴ 999x = 459
x = 459/999 = (17 × 27) / (37 × 27) = 17/37
∴ 0.459459459⋯ is the decimal with 37 in the denominator when represented as rational number
Most Upvoted Answer
Which of the following decimal number is a rational number with denomi...
Solution:
Given that we need to find a rational number with a denominator of 37.
A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not equal to zero.
Let's analyze each option to determine if it is a rational number with a denominator of 37:
a) 0.459459459
To determine if this number is rational with a denominator of 37, we need to check if it can be expressed as a fraction of two integers.
The repeating decimal 0.459459459 can be written as 459/1000.
Since 459 and 1000 are both integers, this decimal number is rational.
Furthermore, 1000 is not divisible by 37, so the denominator is not 37.
Therefore, option 'A' is not the correct answer.
b) 0.459459459
This option is the same as option 'A' and has the same explanation.
Therefore, option 'B' is also not the correct answer.
c) 0.0459459459
To determine if this number is rational with a denominator of 37, we need to check if it can be expressed as a fraction of two integers.
The repeating decimal 0.0459459459 can be written as 45/990.
Since 45 and 990 are both integers, this decimal number is rational.
Furthermore, 990 is divisible by 37, so the denominator is 37.
Therefore, option 'C' is not the correct answer.
d) 0.00459459459
To determine if this number is rational with a denominator of 37, we need to check if it can be expressed as a fraction of two integers.
The repeating decimal 0.00459459459 can be written as 45/9900.
Since 45 and 9900 are both integers, this decimal number is rational.
Furthermore, 9900 is divisible by 37, so the denominator is 37.
Therefore, option 'D' is the correct answer.
In conclusion, the correct answer is option 'D' (0.00459459459) as it is a rational number with a denominator of 37.
Given that we need to find a rational number with a denominator of 37.
A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not equal to zero.
Let's analyze each option to determine if it is a rational number with a denominator of 37:
a) 0.459459459
To determine if this number is rational with a denominator of 37, we need to check if it can be expressed as a fraction of two integers.
The repeating decimal 0.459459459 can be written as 459/1000.
Since 459 and 1000 are both integers, this decimal number is rational.
Furthermore, 1000 is not divisible by 37, so the denominator is not 37.
Therefore, option 'A' is not the correct answer.
b) 0.459459459
This option is the same as option 'A' and has the same explanation.
Therefore, option 'B' is also not the correct answer.
c) 0.0459459459
To determine if this number is rational with a denominator of 37, we need to check if it can be expressed as a fraction of two integers.
The repeating decimal 0.0459459459 can be written as 45/990.
Since 45 and 990 are both integers, this decimal number is rational.
Furthermore, 990 is divisible by 37, so the denominator is 37.
Therefore, option 'C' is not the correct answer.
d) 0.00459459459
To determine if this number is rational with a denominator of 37, we need to check if it can be expressed as a fraction of two integers.
The repeating decimal 0.00459459459 can be written as 45/9900.
Since 45 and 9900 are both integers, this decimal number is rational.
Furthermore, 9900 is divisible by 37, so the denominator is 37.
Therefore, option 'D' is the correct answer.
In conclusion, the correct answer is option 'D' (0.00459459459) as it is a rational number with a denominator of 37.
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Which of the following decimal number is a rational number with denominator 37?a)0.459459459b)0.459459459c)0.0459459459d)0.00459459459Correct answer is option 'A'. Can you explain this answer?
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