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01 Sep 2022, 01:25
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Question Stats:
80% (01:33) correct
20%
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What is the value of \(\sqrt[3]{2.7\%}-\sqrt[4]{0.16\%}\) ?
A. \(0.001\)
B. \(10\%\)
C. \(1\)
D. \(1000\%\)
E. \(100\)
A. \(0.001\)
B. \(10\%\)
C. \(1\)
D. \(1000\%\)
E. \(100\)
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23 Aug 2024, 01:27
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Official Solution:
What is the value of \(\sqrt[3]{2.7\%}-\sqrt[4]{0.16\%}\)?
A. \(0.001\)
B. \(10\%\)
C. \(1\)
D. \(1000\%\)
E. \(100\)
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..
\(\sqrt[3]{2.7\%}-\sqrt[4]{0.16\%}=\)
\(=\sqrt[3]{0.027}-\sqrt[4]{0.0016}=\)
\(=\sqrt[3]{(0.3)^3}-\sqrt[4]{(0.2)^4}=\)
\(=0.3 - 0.2=\)
\(=0.1=\)
\(=10\%\)
Answer: B
What is the value of \(\sqrt[3]{2.7\%}-\sqrt[4]{0.16\%}\)?
A. \(0.001\)
B. \(10\%\)
C. \(1\)
D. \(1000\%\)
E. \(100\)
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.
\(\sqrt[3]{2.7\%}-\sqrt[4]{0.16\%}=\)
\(=\sqrt[3]{0.027}-\sqrt[4]{0.0016}=\)
\(=\sqrt[3]{(0.3)^3}-\sqrt[4]{(0.2)^4}=\)
\(=0.3 - 0.2=\)
\(=0.1=\)
\(=10\%\)
General Discussion
01 Sep 2022, 09:39
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Bunuel
\(\sqrt[3]{2.7\%}-\sqrt[4]{0.16\%}\)
\(\sqrt[3]{0.027}-\sqrt[4]{0.0016}\)
\(\sqrt[3]{(0.3)^3}-\sqrt[4]{(0.2)^4}\)
\(0.3-0.2=0.1 =\frac{10}{100}\) or 10%
B
