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If 3/(10^4) = x%, then x =

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If 3/(10^4) = x%, then x = [#permalink]

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New post 27 May 2016, 05:02
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Difficulty:

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Question Stats:

63% (00:28) correct 37% (00:24) wrong based on 322 sessions

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If \(\frac{3}{10^4}\) = x%, then x =

(A) 0.3
(B) 0.03
(C) 0.003
(D) 0.0003
(E) 0.00003
[Reveal] Spoiler: OA

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Re: If 3/(10^4) = x%, then x = [#permalink]

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New post 27 May 2016, 05:35
nalinnair wrote:
If \(\frac{3}{10^4}\) = x%, then x =

(A) 0.3
(B) 0.03
(C) 0.003
(D) 0.0003
(E) 0.00003



\(\frac{3}{10^4}\) = x%

\(\frac{x}{100}\) = \(\frac{3}{10000}\)

x = \(\frac{3}{100}\) = 0.03

Option B is correct answer.

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Re: If 3/(10^4) = x%, then x = [#permalink]

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New post 30 Nov 2016, 13:52
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nalinnair wrote:
If \(\frac{3}{10^4}\) = x%, then x =

(A) 0.3
(B) 0.03
(C) 0.003
(D) 0.0003
(E) 0.00003


Key Concepts:
#1) We can create equivalent fractions by multiplying or dividing numerator and denominator by the same value.
#2) p/100 = p%. For example, 19/100 = 19%

\(\frac{3}{10^4}\) = \(\frac{3}{10000}\)
Divide numerator and denominator by 100 to get: = \(\frac{0.03}{100}\)
= 0.03%

Answer:
[Reveal] Spoiler:
B

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Re: If 3/(10^4) = x%, then x = [#permalink]

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New post 30 Nov 2016, 14:07
3/(10^4) = x/100....Solve for x
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Re: If 3/(10^4) = x%, then x = [#permalink]

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New post 12 Dec 2016, 15:31
Guys, I'm really confused and here is the origin of my confusion

OG Thought:

X%= (x/100) or 19%= (19/100)

My thought:

X%= (x/ 100) * 100 or 19%= (19/100) * 100 or 19%= .19 * 100

or otherwords, 19/100 doesn't equal 19%, but rather .19. Only when you multiply .19 by 100 does it equal 19%

I swear I'm not trying to be stubborn, maybe my definitional perspective of the question statement if off

Please help!

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Re: If 3/(10^4) = x%, then x = [#permalink]

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New post 13 Dec 2016, 01:51
Expert's post
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SonofaSaracen wrote:
Guys, I'm really confused and here is the origin of my confusion

OG Thought:

X%= (x/100) or 19%= (19/100)

My thought:

X%= (x/ 100) * 100 or 19%= (19/100) * 100 or 19%= .19 * 100

or otherwords, 19/100 doesn't equal 19%, but rather .19. Only when you multiply .19 by 100 does it equal 19%

I swear I'm not trying to be stubborn, maybe my definitional perspective of the question statement if off

Please help!


OG is right.

A percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). It is often denoted using the percent sign, "%", or the abbreviation "pct". Since a percent is an amount per 100, percents can be represented as fractions with a denominator of 100. For example, 25% means 25 per 100, 25/100 and 350% means 350 per 100, 350/100.

Check Percents chapter here: math-number-theory-88376.html
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Re: If 3/(10^4) = x%, then x = [#permalink]

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New post 13 Dec 2016, 02:50
By definition itself, percentage is nothing but amount in each hundred. i.e. 20% mean 20/100 = 0.2
In the equation,
3/10^4 = 0.0003 which is X%. Let's back calculate as I mentioned. What value of X will the equation will give 0.0003.

X% = 0.0003, i.e. X = 0.03. Answer is B.

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Re: If 3/(10^4) = x%, then x = [#permalink]

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New post 23 Aug 2017, 18:13
The key concept for this question is direction of moving decimal places.

Take the numerator 3. , and move the decimal place four places to the left, for you are dividing by 10^4, meaning the numerator will become small by 4 places, which is the number in the exponent.

After moving the decimal four places left, you get 3.0 ---> 0.0003

Now, with 0.0003 you move the decimal two places to the right, because you are multiplying by 100 (i.e. the percent) Since you are multiplying a decimal by a whole number, the value of the decimal becomes larger, hence, 0.0003 x 100 --- move decimal two to right ---> 0.03 = x

Therefore, the answer is (B) 0.03

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If 3/(10^4) = x%, then x = [#permalink]

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New post 23 Aug 2017, 18:41
nalinnair wrote:
If \(\frac{3}{10^4}\) = x%, then x =

(A) 0.3
(B) 0.03
(C) 0.003
(D) 0.0003
(E) 0.00003

\(\frac{3}{10^4}\) = \(\frac{x}{100}\)

\(3 * 10^2 = x * 10^4\)

\(\frac{3 * 10^2}{10^4} = x\)

\(3 * (10^{2-4}) = x\)

\(3 * 10^{-2} = x\)

\(.03 = x\)

Answer B

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If 3/(10^4) = x%, then x =   [#permalink] 23 Aug 2017, 18:41
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