Question

continue dividing on the algorithm. what is 40 hundredths divided by 9 ones?
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$$\begin{array}{r}0.4\\square\\\\9\\overline{)4.00}\\\\-3.6\\downarrow\\\\\\hline.40\\\\-.\\square\\square\\\\.\\square\\square\\end{array}$$

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1 2 3 4 5 6 7 8 9 0 enter

Explanation:

Step1: Analyze the division

We have \(0.40\) (which is 40 hundredths) divided by 9. We know that \(9\times0.04 = 0.36\), but wait, actually we are looking at the division of \(4.00\) by \(9\) in the long division. After the first step, we have a remainder of \(0.40\) (40 hundredths). Now we need to find how many times 9 goes into 40 hundredths.

Step2: Find the digit

We know that \(9\times4 = 36\), so \(9\times0.04 = 0.36\) (since we are in the hundredths place). Wait, no, the current place is the thousandths? Wait, no, the dividend is \(4.00\), divisor \(9\). The first digit after decimal is \(4\) (tenths place: \(9\times0.4 = 3.6\)), remainder \(0.4\). Then we bring down the 0, making it \(0.40\) (40 hundredths). Now we need to find \(0.40\div9\). \(9\times0.04 = 0.36\), so the next digit (hundredths place) is \(4\).

Answer:

The digit in the square (hundredths place of the quotient) is \(4\). So the quotient becomes \(0.44\) (after this step), and the subtraction part is \( - 0.36\) (since \(9\times0.04 = 0.36\)), and the new remainder is \(0.40 - 0.36 = 0.04\). But for the square in the quotient (the digit we need to find), it's \(4\).