Which one of the following is nearest to 0.313233 ?

Options

A. `3//10`
B. `31//1000`
C. `313//1000`
D. `31323//100000`

Answer

To find which of the given options is nearest to 0.313233, we will convert each option into decimal form and then compare them to 0.313233.

### Step 1: Convert each option to decimal form.

**Option A: \( \frac{3}{10} \)**
To convert this fraction to decimal:
\[ \frac{3}{10} = 0.3 \]

**Option B: \( \frac{31}{1000} \)**
To convert this fraction to decimal:
\[ \frac{31}{1000} = 0.031 \]

**Option C: \( \frac{313}{1000} \)**
To convert this fraction to decimal:
\[ \frac{313}{1000} = 0.313 \]

**Option D: \( \frac{31323}{100000} \)**
To convert this fraction to decimal:
\[ \frac{31323}{100000} = 0.31323 \]

### Step 2: Compare each decimal with 0.313233.

Now we will compare each calculated decimal with 0.313233:

- **Option A:** \( 0.3 \)
- **Option B:** \( 0.031 \)
- **Option C:** \( 0.313 \)
- **Option D:** \( 0.31323 \)

### Step 3: Determine which decimal is closest to 0.313233.

Now we will find the absolute difference between each decimal and 0.313233:

- **Difference for Option A:**
\[ |0.3 - 0.313233| = 0.013233 \]

- **Difference for Option B:**
\[ |0.031 - 0.313233| = 0.282233 \]

- **Difference for Option C:**
\[ |0.313 - 0.313233| = 0.000233 \]

- **Difference for Option D:**
\[ |0.31323 - 0.313233| = 0.000003 \]

### Step 4: Identify the smallest difference.

From the differences calculated, we see:

- Option A: \( 0.013233 \)
- Option B: \( 0.282233 \)
- Option C: \( 0.000233 \)
- Option D: \( 0.000003 \)

The smallest difference is for **Option D** \( 0.000003 \).

### Conclusion:

Thus, the option that is nearest to 0.313233 is **Option D: \( \frac{31323}{100000} \)**.

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