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Directions: Your answer may be an integer, a decimal, or a fraction, and it may be negative. Enter the exact answer unless the question asks you to round your answer.


Q. When the decimal point of a certain positive decimal number is moved six places to the right, the resulting number is 9 times the reciprocal of the original number. What is the original number?

Correct answer is '0.003'. Can you explain this answer?
Most Upvoted Answer
Directions: Your answer may be an integer, a decimal, or a fraction, a...

Understanding the problem:
The problem states that when the decimal point of a positive decimal number is moved six places to the right, the resulting number is 9 times the reciprocal of the original number.

Solving the problem:
Let the original decimal number be x. When we move the decimal point six places to the right, we get 1000000x (since moving the decimal point to the right by n places is equivalent to multiplying by 10^n).

According to the problem, 1000000x = 9(1/x) [since the resulting number is 9 times the reciprocal of the original number]

Solving this equation:
1000000x = 9/x
=> 1000000x^2 = 9
=> x^2 = 9/1000000
=> x = sqrt(9/1000000)

Calculating the original number:
x = sqrt(9/1000000)
x = sqrt(9)/sqrt(1000000)
x = 3/1000
x = 0.003

Therefore, the original number is 0.003.
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Community Answer
Directions: Your answer may be an integer, a decimal, or a fraction, a...
Moving the decimal point of a positive decimal number, n, six places to the right is
equivalent to multiplying n by 106. In the question, you are given that the result of such a change is 9 times the reciprocal of the original number, or 9(1/n). Therefore n(106) = 9(1/n). You can solve this equation for n as follows.
The correct answer is 0.003.
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Directions: Your answer may be an integer, a decimal, or a fraction, and it may be negative. Enter the exact answer unless the question asks you to round your answer.Q. When the decimal point of a certain positive decimal number is moved six places to the right, the resulting number is 9 times the reciprocal of the original number. What is the original number?Correct answer is '0.003'. Can you explain this answer?
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