Place Value Problem: Constructing a Number with 7 Hundreds, 1 Ten, and 8 Ones

To solve this problem, we need to construct a number using the digits provided for specific place values.

• Step 1: Identify the place values: ones, tens, and hundreds.
• Step 2: Allocate the digits to the correct place values:
  - Ones digit: $8$
  - Tens digit: $1$
  - Hundreds digit: $7$
• Step 3: Combine these according to place value to form the number.

Thus, we construct the number by starting from the highest place value to the lowest:
Hundreds place: $7$
Tens place: $1$
Ones place: $8$

Hence, the number formed by these place values is $718$.

Therefore, the correct solution is $718$.