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17 May 2022, 08:38
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E
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Difficulty:
25%
(medium)
Question Stats:
84% (00:35) correct
16%
(00:30)
wrong
based on 31
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What is the value of \(\sqrt{16\%}\)?
A. \(0.004\%\)
B. \(0.04\%\)
C. \(0.4\%\)
D. \(4\%\)
E. \(40\%\)
A. \(0.004\%\)
B. \(0.04\%\)
C. \(0.4\%\)
D. \(4\%\)
E. \(40\%\)
17 May 2022, 08:38
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Bookmarks
Official Solution:
What is the value of \(\sqrt{16\%}\)?
A. \(0.004\%\)
B. \(0.04\%\)
C. \(0.4\%\)
D. \(4\%\)
E. \(40\%\)
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..
So, what's the answer? 4%? Just 4? 0.4%? Let's see.
Convert to a ratio:
\(\sqrt{16\%}=\sqrt{\frac{16}{100}}=\frac{4}{10}\).
Notice that the answer choices are as a percentage, so to get "%" symbol, to convert the ratio into a percentage, just multiply by 100%:
\(\frac{4}{10}=\frac{4}{10}*100\%=40\%\).
Answer: E
What is the value of \(\sqrt{16\%}\)?
A. \(0.004\%\)
B. \(0.04\%\)
C. \(0.4\%\)
D. \(4\%\)
E. \(40\%\)
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..
So, what's the answer? 4%? Just 4? 0.4%? Let's see.
Convert to a ratio:
\(\sqrt{16\%}=\sqrt{\frac{16}{100}}=\frac{4}{10}\).
Notice that the answer choices are as a percentage, so to get "%" symbol, to convert the ratio into a percentage, just multiply by 100%:
\(\frac{4}{10}=\frac{4}{10}*100\%=40\%\).
Answer: E
