Question

the decimal representation of \\(\frac{8}{11}\\) will be less than 1, because youre dividing 8 by 11. now youre ready to start dividing. 8 ones have been unbundled for 80 tenths. divide 80 tenths by 11. then, multiply to show how many tenths you shared. finally, subtract to show how many tenths you have left over. \\(\frac{8}{11}\\) \\(\

$$\begin{array}{r}0.\\square\\\\11\\overline{)8.0}\\\\-\\square.\\square\\\\\\hline.\\square\\end{array}$$

\\)

Explanation:

Step1: Find tenths quotient digit

We divide 80 tenths by 11. The largest integer $n$ where $11n \leq 80$ is 7, since $11 \times 7 = 77$. So the tenths digit is 7.

Step2: Calculate subtracted value

Multiply the divisor 11 by the tenths digit 7: $11 \times 0.7 = 7.7$

Step3: Compute remainder

Subtract the result from 8.0: $8.0 - 7.7 = 0.3$

Answer:

The filled-in long division is:

$$\begin{array}{r} 0.7 \\ 11 \enclose{longdiv}{8.0} \\ \underline{-7.7} \\ 0.3 \end{array}$$

So the tenths place is 7, the subtracted value is 7.7, and the remainder is 0.3.