Final answer:
Irrational numbers such as π (pi) cannot be written as a fraction, but scientific notation allows for the concise representation of very large or small numbers without suggesting whether they are rational or irrational.
Step-by-step explanation:
The given statement '{x is real but not rational} {3.14159....}cannot be written as a fraction' is indicating that numbers like π (pi), which is represented here as 3.14159..., are irrational numbers and cannot be expressed as a fraction. In contrast, scientific notation is a way to write very large or very small numbers in a more compact form, such as writing 0.0000045 as 4.5 x 10-6. This notation doesn't imply that the number is rational or irrational; it's just a convenient representation.
It should be noted that irrational numbers, like the approximated value of π given, cannot be precisely expressed as a fraction or with a finite decimal representation. They can be approximated as fractions for practical purposes, but the approximation is not exact. For example, we can approximate π as 22/7 or use scientific notation to express small approximations of π, like 3.14 x 100, but neither of these are exact representations of π.