Question

When the decimal point of a certain positive integer is moved 4 places to the left, the resulting number is 16 times the reciprocal of the
original number. What is the original number?​

Answer 1

Answer:

Moving the decimal point of a positive decimal number, n, six places to the right is equivalent to multiplying n by 106106. In the question, you are given that the result of such a change is 9 times the reciprocal of the original number, or 9(1n)9(1n). Therefore n(106)=9(1n)n(106)=9(1n). You can solve this equation for n as follows.

n(106)=9(1n)n(106)=9(1n)

n2=9(106)n2=9(106)

n=0.003n=0.003.

Step-by-step explanation:

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Answer 2

Answer:

400

Step-by-step explanation:

Translate the informtion in the problem into an equation and solve. Let the original number be x.

Moving the decimal point of the original number 4 places to the left is equivalent to multiplying the number by 0.0001 or 1/10,000.

So, the left side of the equation is x.

For the right side of the equation, multiply 16 by the reciprocal of x to get: 16 (1/x).

(1/10,000)x = 16 (1/x)

cross multiple 10,000 multiplied by 16 = 1,60,000.

x square = 1,60,000

√1,60,000 = 400

x = 400