Assertion : `0.271` is a terminating decimal and we can express this number as `271//1000` which is of the form p/q, where p and q are integers and `q ne 0` .
Reason : A terminating or non-terminating decimal expansion can be expressed as rational number .

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion .
B. If both assertion and reason are true but reason is not the correct explanation of assertion .
C. If assertion is true but reason is false.
D. If assertion is false but reason is true .

Answer

To solve the assertion and reason provided in the question, we will analyze each statement step by step.

### Step 1: Understanding the Assertion
The assertion states that `0.271` is a terminating decimal and can be expressed as `271/1000`.

- A terminating decimal is a decimal that has a finite number of digits after the decimal point.
- The number `0.271` has three digits after the decimal point, which confirms that it is indeed a terminating decimal.

### Step 2: Expressing `0.271` as a Fraction
To express `0.271` as a fraction:

1. Write `0.271` as `271` divided by `1000` because there are three digits after the decimal point.
\[ 0.271 = \frac{271}{1000} \]

2. Here, `271` is the numerator (p) and `1000` is the denominator (q). Since `1000` is not equal to `0`, this fraction is valid.

### Step 3: Understanding the Reason
The reason states that a terminating or non-terminating decimal expansion can be expressed as a rational number.

- A rational number is defined as any number that can be expressed in the form `p/q`, where `p` and `q` are integers and `q` is not zero.
- All terminating decimals can be expressed as rational numbers. However, not all non-terminating decimals can be expressed as rational numbers. Only non-terminating repeating decimals can be expressed as rational numbers, while non-terminating non-repeating decimals cannot.

### Step 4: Conclusion
- The assertion is **true** because `0.271` is a terminating decimal and can be expressed as `271/1000`.
- The reason is **partially true** because while all terminating decimals can be expressed as rational numbers, not all non-terminating decimals can. Therefore, the statement "A terminating or non-terminating decimal expansion can be expressed as a rational number" is misleading.

### Final Answer
- The assertion is true, and the reason is incorrect.

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