Question

sean says that \\(\frac{9}{40} = 0.\overline{2}\\). do you agree with sean? yes, the digit 2 is repeating in the quotient. no, sean needs to keep dividing.

Explanation:

Step1: Analyze the division process

To convert \(\frac{9}{40}\) to a decimal, we perform long division. We have \(9\div40\). We add a decimal point and zeros: \(9.000\div40\).
First, \(40\) goes into \(90\) (after adding the decimal) \(2\) times (\(40\times2 = 80\)), subtract \(80\) from \(90\) to get \(10\). Then we bring down a \(0\) to make \(100\). \(40\) goes into \(100\) \(2\) times (\(40\times2=80\)), subtract \(80\) from \(100\) to get \(20\). Then we bring down another \(0\) to make \(200\).

Step2: Continue the division

\(40\) goes into \(200\) \(5\) times (\(40\times5 = 200\)), so the division would be \(0.225\), not a repeating decimal with just \(2\) repeating. Sean stopped too early. So we need to keep dividing to get the correct decimal. So Sean's statement that \(\frac{9}{40}=0.\overline{2}\) is incorrect because we can continue dividing and get a terminating decimal (or see that the remainder will eventually be zero or repeat in a different way). So we do not agree with Sean, he needs to keep dividing.

Answer:

No, Sean needs to keep dividing.