To solve these expressions, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

For the first expression:
13.17 - 256 ÷ 16 + 14 ÷ 7 - 1

First, we perform the division:
13.17 - 16 + 2 - 1

Next, we perform the subtraction and addition:
-2.83

Therefore, the value of the first expression is -2.83.

For the second expression:
15 - 25 × 9 ÷ (100 × 2)

First, we perform the multiplication and division within the parentheses:
15 - 25 × 9 ÷ 200

Next, we perform the multiplication and division from left to right:
15 - 2.25

Finally, we perform the subtraction:
12.75

Therefore, the value of the second expression is 12.75.