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# What is the least integer n such that 1/2^n < 0.001 ?

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Re: What is the least integer n such that 1/2^n < 0.001 ? [#permalink]
Bunuel wrote:
What is the least integer n such that $$\frac{1}{2^n} < 0.001$$ ?

A) 10

B) 11

C) 500

D) 501

E) There is no such least integer

Solution:

Notice that 0.001 = 1/1000.

Since 2^9 = 512 and 2^10 = 1024, then 1/(2^9) = 1/512 > 1/1000 but 1/(2^10) = 1/1024 < 1/1000. Therefore, the least integer value of n is 10.

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Re: What is the least integer n such that 1/2^n < 0.001 ? [#permalink]
1 / ( 2^n) < .001

1 / ( 2^n) < 1 * (10)^-3

1 / (2^n) < 1 / (10^3)

Rule: For (+)Positive Fractions, given the SAME NUMERATOR, the Larger the Denominator gets, the Smaller the Value of the (+)Pos. Fraction will be

thus we need to find the MINIMUM Integer = n -----> in which:

(2)^n > (10)^3
(2)^n > 1,000

the first Integer Power will be N = 10

(2)^10 = 1024

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Re: What is the least integer n such that 1/2^n < 0.001 ? [#permalink]
$$\frac{1 }{ (2^n)}$$ < 0.001

=> $$\frac{1 }{ (2^n)}$$ < $$\frac{1 }{ 1000}$$

=> 1000 < $$2^n$$

For n = 10: $$2^{10}$$ = 1024

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Re: What is the least integer n such that 1/2^n < 0.001 ? [#permalink]
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Re: What is the least integer n such that 1/2^n < 0.001 ? [#permalink]
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