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Math Expert V
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5√2 percent of 1/√200 =  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 72% (01:06) correct 28% (01:13) wrong based on 91 sessions

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$$5√2$$ percent of $$\frac{1}{√200} =$$

A. 0.005
B. 0.02
C. 0.05
D. 0.2
E. 0.5

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5√2 percent of 1/√200 =  [#permalink]

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(5\sqrt{2})/100) * 1/(10*\sqrt{2}) = 0.005

Option A
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Joined: 12 Sep 2015
Posts: 4017
Re: 5√2 percent of 1/√200 =  [#permalink]

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Top Contributor
Bunuel wrote:
$$5√2$$ percent of $$\frac{1}{√200} =$$

A. 0.005
B. 0.02
C. 0.05
D. 0.2
E. 0.5

p percent = p/100
For example, 19% = 19/100
So, 5√2 percent = (5√2)/100

√200 = (√100)(√2) = 10√2

So, 5√2 percent of 1/√200 = [(5√2)/100][1/10√2]
= [5/100][1/10] [the √2's cancel out]
= 5/1000
= 0.005

Cheers,
Brent
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Senior SC Moderator V
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5√2 percent of 1/√200 =  [#permalink]

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Bunuel wrote:
$$5√2$$ percent of $$\frac{1}{√200} =$$

A. 0.005
B. 0.02
C. 0.05
D. 0.2
E. 0.5

I. Arithmetic
Change the denominator either initially* or while solving, as here

Setup: 10 percent of $$\frac{1}{2}=$$
LHS: $$(\frac{10}{100}*\frac{1}{2})$$

$$5√2$$ percent of $$\frac{1}{√200}$$:

$$(\frac{5\sqrt{2}}{100}*\frac{1}{\sqrt{200}})=\frac{5\sqrt{2}}{100*\sqrt{200}}=$$

$$\frac{5\sqrt{2}}{100*\sqrt{100*2}}=$$

$$\frac{5\sqrt{2}}{100*10\sqrt{2}}=$$

$$\frac{5}{100*10}=\frac{1}{100*2}=\frac{1}{200}=$$

$$0.005$$

II. Approximate in pieces

$$5√2$$ percent of $$\frac{1}{√200}$$?

(1) $$5\sqrt{2}\approx{(5*1.4)}\approx{7}$$

$$7$$ percent =$$0.07$$

(2) $$\frac{1}{\sqrt{200}}$$:
the denominator is between 14 and 15. $$14^2=196$$, and $$15^2=225$$

$$\sqrt{196}<\sqrt{200}<\sqrt{225}$$

$$\sqrt{200}$$ is closer to 14:
$$\frac{1}{\sqrt{200}}\approx{\frac{1}{14}}\approx{0.07}$$

(3) Together: 7 percent of 0.07 =

$$(0.07*0.07)=0.0049$$

$$\approx{0.005}$$

*$$\frac{1}{\sqrt{200}}$$
Change the denominator
$$\sqrt{200}=\sqrt{100*2}=10\sqrt{2}=>$$
$$\frac{1}{\sqrt{200}}= \frac{1}{10\sqrt{2}}$$

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Re: 5√2 percent of 1/√200 =  [#permalink]

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Bunuel wrote:
$$5√2$$ percent of $$\frac{1}{√200} =$$

A. 0.005
B. 0.02
C. 0.05
D. 0.2
E. 0.5

We can express 5√2 percent as 5√2/100. Thus, we have:

(5√2)/100 x (1/√200) = (5√2)/(100√200) =1/(20 x 10) = 1/200 = 0.005

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: 5√2 percent of 1/√200 =   [#permalink] 19 Oct 2018, 15:21
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