To solve the expression \(8 \times 1000 + 4 \times 100 + 7 \times 10 + 1 \times 1 + 7 \times \frac{1}{10}\), we will calculate each term individually:
- \(8 \times 1000 = 8000\)
- \(4 \times 100 = 400\)
- \(7 \times 10 = 70\)
- \(1 \times 1 = 1\)
- \(7 \times \frac{1}{10} = 0.7\)
Now, we will add these results together:
\[ 8000 + 400 + 70 + 1 + 0.7 \]
First, add \(8000\) and \(400\):
\[ 8000 + 400 = 8400 \]
Next, add \(70\):
\[ 8400 + 70 = 8470 \]
Next, add \(1\):
\[ 8470 + 1 = 8471 \]
Finally, add \(0.7\):
\[ 8471 + 0.7 = 8471.7 \]
So, the final result is:
\[ \boxed{8471.7} \]