Find the quotient 43.782 ÷ 6.

Step-by-step solution

1. 1

   Notice the divisor is already a whole number. When only the dividend carries a decimal point, no rescaling is needed: you can divide exactly as with whole numbers and simply keep the decimal point of the quotient directly above the decimal point of the dividend.

2. 2

   Divide digit by digit. Working left to right on $43.782\div 6$:

   $43\div 6=7$ remainder $1$ → first digit $7$, carry $1$;

   $17\div 6=2$ remainder $5$ → next digit $2$;

   $58\div 6=9$ remainder $4$ → next digit $9$;

   $42\div 6=7$ remainder $0$ → last digit $7$.

3. 3

   Place the decimal point. The digits produced are $7,2,9,7$ and the point sits after the first of them, because $43$ (the integer part) was consumed first:

   $43.782\div 6=7.297$

4. 4

   Check by multiplying back. Division and multiplication are inverse operations, so the quotient times the divisor must return the dividend:

   $7.297\times 6=43.782$

   $\boxed{7.297}$

5. 5

   Estimate to confirm the size. $42\div 6=7$, so the answer had to be a little more than $7$ — which rules out common slips such as $72.97$ or $0.7297$ caused by misplacing the decimal point.