Final answer:
IEEE 754 floating-point representations are less precise than integers when dealing with large numbers because they round the number to fit within a set number of bits. This approximation can become a problem in scientific work where high precision is required, as opposed to integers that can represent values exactly up to the limit of their size.
Step-by-step explanation:
An example where IEEE 754 encoded values are less precise than integers can be illustrated when dealing with very large numbers. For instance, consider the integer value 12345678901234567890. In a floating-point system like IEEE 754, this number cannot be represented precisely and would be rounded to something like 1.23456789012345×1019, which lacks the precision of the original integer.
IEEE 754 floating-point numbers have a fixed number of bits for storing numbers, which means that they can only approximate numbers up to a certain level of precision. Integers, on the other hand, can represent numbers exactly up to the limit of their size (which for modern computers is typically 32 or 64 bits).
The difference in precision is significant in computational tasks where the exact value is crucial. In operations involving significant figures, results are often rounded based on the least precise figure involved. For scientific work, where a high level of detail is necessary, this rounding makes floating-point numbers less reliable than integers.