Question

Irrational numbers, like 0.01020304..., can be written as a fraction.

False, any decimal that does not terminate or repeat is rational
True, all decimals can be written as a fraction
False, any decimal that does not terminate or repeat cannot be written as a fraction
True, decimals that do not terminate can always be written as a fraction

Answer 1

The statement "Irrational numbers, like 0.01020304..., can be written as a fraction" is **False**.

Here’s a breakdown of the provided statements to clarify:

1. **False, any decimal that does not terminate or repeat is rational**: This statement is false; it is the opposite of the truth. Decimals that do not terminate and do not repeat are considered irrational.

2. **True, all decimals can be written as a fraction**: This statement is misleading; not all decimals can be written as a fraction. Only rational numbers can be expressed as fractions.

3. **False, any decimal that does not terminate or repeat cannot be written as a fraction**: This statement is true. Any decimal that is non-terminating and non-repeating is an irrational number and cannot be expressed as a fraction.

4. **True, decimals that do not terminate can always be written as a fraction**: This statement is false. Only terminating or repeating decimals can be written as fractions.

In conclusion, the correct understanding is that non-terminating, non-repeating decimals represent irrational numbers and cannot be expressed as fractions.