SOLUTION: When the decimal point of a certain positive decimal number ismoved four places to the right, the newnumber is four times the reciprocal of the original number.Theoriginal numbe

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Question 732206: When the decimal point of a certain positive
decimal number ismoved four places to the right,
the newnumber is four times the reciprocal of the
original number.Theoriginal number, is
please send me step by step
Found 3 solutions by lynnlo, ikleyn, MathTherapy:
Answer by lynnlo(4176) About Me  (Show Source):
You can put this solution on YOUR website!
STEP BY STEP

Answer by ikleyn(53339) About Me  (Show Source):
You can put this solution on YOUR website!
.
When the decimal point of a certain positive
decimal number is moved four places to the right,
the new number is four times the reciprocal of the
original number. The original number is . . .
please send me step by step
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the original number.

Then the new number is  10%5E4%2Ax.


Your equation for 'x' is THIS

    10%5E4%2Ax = 4%2Fx.


It implies

    10%5E4%2Ax%5E2 = 4,

    x%5E2 = 4%2F10%5E4,

    x = sqrt%284%2F10%5E4%29 = 2%2F10%5E2 = 2%2F100 = 1%2F50 = 0.02.


ANSWER.  The original number is  2%2F100 = 1%2F50 = 0.02.

Solved step by step, on your request.



Answer by MathTherapy(10579) About Me  (Show Source):
You can put this solution on YOUR website!
When the decimal point of a certain positive decimal number ismoved four places to the right, the newnumber is four
times the reciprocal of the original number.Theoriginal number, is

please send me step by step

Let number be N
Moving a number 4 (FOUR) decimal places to the right is the equivalent of multiplying the number by 10%5E4, or by 10,000
So, moving the number 4 places to the right makes it 10%5E4+%2A+N, or 10,000N
We then get: 10%5E4N+=+4%281%2FN%29
             10%5E4N+=+4%2FN
            10%5E4N%5E2+=+4 ---- Cross-multiplying
               N%5E2+=+4%2F10%5E4
             matrix%281%2C3%2C+sqrt%28N%5E2%29%2C+%22=%22%2C+0+%2B-sqrt%284%2F10%5E4%29%29 ---- Taking square root of both sides
                 N = 2%2F10%5E2+=+2%2F100 <=== N is POSITIVE (> 0)
Number, in DECIMAL form, or highlight_green%28N+=+highlight%28.02%29%29