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What is the value of \(\sqrt{(\frac{1}{50})\%}=\)?
A. \((\frac{1}{\sqrt{2}})\%\)
B. \((\sqrt{2})\%\)
C. \(2\%\)
D. \(20\%\)
E. \(200\%\)
A. \((\frac{1}{\sqrt{2}})\%\)
B. \((\sqrt{2})\%\)
C. \(2\%\)
D. \(20\%\)
E. \(200\%\)
17 May 2022, 08:32
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Bookmarks
Official Solution:
What is the value of \(\sqrt{(\frac{1}{50})\%}=\)?
A. \((\frac{1}{\sqrt{2}})\%\)
B. \((\sqrt{2})\%\)
C. \(2\%\)
D. \(20\%\)
E. \(200\%\)
Worth knowing that "per cent" from Latin literally means "per one hundred" or "out of one hundred", so for example, \(x\%\) is \(\frac{x}{100}\) (\(x\) per one hundred) and say \(5\%\) is \(\frac{5}{100} = 0.05\) (5 out of one hundred). On the other hand, we can write 0.05 as \(0.05*100\% = 5\%\) and say 20 as \(20*100\% = 2000\%\).
Basically, "%" symbol just means "per 100", or algebraically, "/100". Thus:
To drop "%" symbol, so to convert the percentage into a ratio, just divide by 100: \(m\% = \frac{m}{100}\). For example, \(10\%=\frac{10}{100}=\frac{1}{10}=0.1\) and \(400\%=\frac{400}{100}=4\).
To get "%" symbol, so to convert the ratio into a percentage, just multiply by 100%: \(n=n*100\%\) (100% is just 100/100 = 1, so we are essentially multiplying by 1). For example, \(0.4=0.4*100\%=40\%\) and \(15=15*100\%=1500\%\).
To sum up: \(x\%\) and \(\frac{x}{100}\) are just two different ways of writing the same thing: as a percentage and as a ratio.
Back to the question..
First of all notice that \(\frac{1}{50}=\frac{2}{100}\) and next, convert to a ratio:
\(\sqrt{(\frac{1}{50})\%}=\sqrt{(\frac{2}{100})\%}=\sqrt{\frac{(\frac{2}{100})}{100}}=\sqrt{\frac{2}{100^2}}=\frac{\sqrt{2}}{100}\)
Notice that the answer choices are as a percentage, so to get "%" symbol, to convert the ratio into a percentage, just multiply by 100%:
\(\frac{\sqrt{2}}{100}=\frac{\sqrt{2}}{100}*100\%=\sqrt{2}\%\)
Answer: B
What is the value of \(\sqrt{(\frac{1}{50})\%}=\)?
A. \((\frac{1}{\sqrt{2}})\%\)
B. \((\sqrt{2})\%\)
C. \(2\%\)
D. \(20\%\)
E. \(200\%\)
Worth knowing that "per cent" from Latin literally means "per one hundred" or "out of one hundred", so for example, \(x\%\) is \(\frac{x}{100}\) (\(x\) per one hundred) and say \(5\%\) is \(\frac{5}{100} = 0.05\) (5 out of one hundred). On the other hand, we can write 0.05 as \(0.05*100\% = 5\%\) and say 20 as \(20*100\% = 2000\%\).
Basically, "%" symbol just means "per 100", or algebraically, "/100". Thus:
To drop "%" symbol, so to convert the percentage into a ratio, just divide by 100: \(m\% = \frac{m}{100}\). For example, \(10\%=\frac{10}{100}=\frac{1}{10}=0.1\) and \(400\%=\frac{400}{100}=4\).
To get "%" symbol, so to convert the ratio into a percentage, just multiply by 100%: \(n=n*100\%\) (100% is just 100/100 = 1, so we are essentially multiplying by 1). For example, \(0.4=0.4*100\%=40\%\) and \(15=15*100\%=1500\%\).
To sum up: \(x\%\) and \(\frac{x}{100}\) are just two different ways of writing the same thing: as a percentage and as a ratio.
Back to the question..
First of all notice that \(\frac{1}{50}=\frac{2}{100}\) and next, convert to a ratio:
\(\sqrt{(\frac{1}{50})\%}=\sqrt{(\frac{2}{100})\%}=\sqrt{\frac{(\frac{2}{100})}{100}}=\sqrt{\frac{2}{100^2}}=\frac{\sqrt{2}}{100}\)
Notice that the answer choices are as a percentage, so to get "%" symbol, to convert the ratio into a percentage, just multiply by 100%:
\(\frac{\sqrt{2}}{100}=\frac{\sqrt{2}}{100}*100\%=\sqrt{2}\%\)
Answer: B
