Which among the following is the smallest unit of time ?

Options

A. second
B. millenium
C. nanosecond
D. microsecond

Answer

To determine the smallest unit of time among the options provided (millennium, second, nanosecond, and microsecond), we can analyze each unit step by step.

### Step-by-Step Solution:

1. **Understanding the Units**:
- **Millennium**: This is a period of 1,000 years. In seconds, it can be calculated as:
\[ 1 \text{ millennium} = 1,000 \text{ years} = 1,000 \times 365 \times 24 \times 60 \times 60 \text{ seconds} \]
- **Second**: This is the base unit of time in the International System of Units (SI).
- **Microsecond**: This is one-millionth of a second, or \(10^{-6}\) seconds.
- **Nanosecond**: This is one-billionth of a second, or \(10^{-9}\) seconds.

2. **Comparing the Sizes**:
- **Millennium**: As calculated, this is a very large unit of time.
- **Second**: This is a standard unit of time.
- **Microsecond**: This is smaller than a second, specifically \(0.000001\) seconds.
- **Nanosecond**: This is smaller than a microsecond, specifically \(0.000000001\) seconds.

3. **Ordering the Units**:
- From largest to smallest, we have:
- Millennium (largest)
- Second
- Microsecond
- Nanosecond (smallest)

4. **Conclusion**:
- Among the given options, the smallest unit of time is the **nanosecond**.

### Final Answer:
The smallest unit of time among the options is **nanosecond**.

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