The number $\sqrt{0.0001}$ is :

Q: The number $\sqrt{0.0001}$ is :

The number $\sqrt{0.0001}$ is indeed a rational number, which supports Option 2 as the correct answer. Let's break down the reasoning: 1. **Explanation for Option 2 (Correct Answer):** - A rational number is defined as any number that can be expressed as the quotient or fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. - The number $0.0001$ can be expressed as $\frac{1}{10000}$. - The square root of $\frac{1}{10000}$ is $\frac{1}{100}$, which is equal to $0.01$. - Since $0.01$ can be expressed as $\frac{1}{100}$, it is a rational number. - Therefore, $\sqrt{0.0001} = 0.01$ is a rational number, confirming that Option 2 is correct. 2. **Explanation for why each of the other options is incorrect:** - **Option 1: A rational number less than 0.01.** - As calculated, $\sqrt{0.0001} = 0.01$, which is not less than 0.01. Therefore, this option is incorrect. - **Option 3: An irrational number.** - An irrational number cannot be expressed as a simple fraction. Since $\sqrt{0.0001} = 0.01$ and can be expressed as $\frac{1}{100}$, it is not irrational. Thus, this option is incorrect. - **Option 4: Neither a rational number nor an irrational number.** - Every real number is either rational or irrational. Since $\sqrt{0.0001} = 0.01$ is a rational number, this option is incorrect. In conclusion, the correct answer is Option 2, as $\sqrt{0.0001}$ is a rational number.

Question

Accepted Answer

The number $\sqrt{0.0001}$ is indeed a rational number, which supports Option 2 as the correct answer. Let's break down the reasoning:

1. **Explanation for Option 2 (Correct Answer):**
   - A rational number is defined as any number that can be expressed as the quotient or fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.
   - The number $0.0001$ can be expressed as $\frac{1}{10000}$.
   - The square root of $\frac{1}{10000}$ is $\frac{1}{100}$, which is equal to $0.01$.
   - Since $0.01$ can be expressed as $\frac{1}{100}$, it is a rational number.
   - Therefore, $\sqrt{0.0001} = 0.01$ is a rational number, confirming that Option 2 is correct.

2. **Explanation for why each of the other options is incorrect:**

- **Option 1: A rational number less than 0.01.**
     - As calculated, $\sqrt{0.0001} = 0.01$, which is not less than 0.01. Therefore, this option is incorrect.

- **Option 3: An irrational number.**
     - An irrational number cannot be expressed as a simple fraction. Since $\sqrt{0.0001} = 0.01$ and can be expressed as $\frac{1}{100}$, it is not irrational. Thus, this option is incorrect.

- **Option 4: Neither a rational number nor an irrational number.**
     - Every real number is either rational or irrational. Since $\sqrt{0.0001} = 0.01$ is a rational number, this option is incorrect.

In conclusion, the correct answer is Option 2, as $\sqrt{0.0001}$ is a rational number.