Official Solution:What is the value of \(\sqrt{(49\%)} -\frac{7}{100}\) ?A. 0
B. 0.63%
C. 0.063
D. 63%
E. 6.3
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..
\(\sqrt{(49\%)} -\frac{7}{100}=\)
\(=\sqrt{\frac{49}{100}} -\frac{7}{100}=\)
\(=\frac{7}{10} -\frac{7}{100}=\)
\(=\frac{70}{100} -\frac{7}{100}=\)
\(=\frac{63}{100} =\)
\(=63\%\)
Answer: D