The decimal expansion of every rational number is either ________ or non-terminating _________

Answer

To answer the question, "The decimal expansion of every rational number is either ________ or non-terminating _________", we need to fill in the blanks with the appropriate terms.

### Step-by-Step Solution:

1. **Understanding Rational Numbers**:
- A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

2. **Types of Decimal Expansions**:
- Decimal expansions can be classified into two main types:
- **Terminating Decimals**: These are decimals that come to an end after a finite number of digits. For example, the rational number \( \frac{1}{4} = 0.25 \) is a terminating decimal.
- **Non-Terminating Decimals**: These are decimals that continue indefinitely. However, they can be further classified into:
- **Recurring Decimals**: These are non-terminating decimals that have a repeating pattern. For example, \( \frac{1}{3} = 0.333...\) (where '3' repeats indefinitely) is a recurring decimal.

3. **Filling in the Blanks**:
- Based on the definitions above, we can fill in the blanks in the statement:
- The decimal expansion of every rational number is either **terminating** or non-terminating **recurring**.

### Final Answer:
The decimal expansion of every rational number is either **terminating** or non-terminating **recurring**.