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To find the difference between one-third and 0.333 without a calculator, let's break it down step by step:

### Step 1: Represent one-third as a decimal
One-third is represented as a repeating decimal:
\[
\frac{1}{3} = 0.33333\ldots
\]
This is an infinite repeating decimal, where the digit 3 repeats indefinitely.

### Step 2: Compare with the given decimal
The decimal provided in the question is 0.333, which has only three decimal places and **is not the same** as \(\frac{1}{3}\). Therefore, we need to subtract 0.333 from the exact value of \(\frac{1}{3}\).

### Step 3: Subtract 0.333 from \(\frac{1}{3}\)
We calculate the difference between \(\frac{1}{3}\) and 0.333. The repeating decimal for \(\frac{1}{3}\) can be written as \(0.33333\ldots\).

Now, subtract the two values:
\[
\frac{1}{3} - 0.333 = 0.33333\ldots - 0.333 = 0.00033\ldots
\]
The difference is approximately 0.00033 (with more 3's repeating).

### Step 4: Convert the difference to a fraction
The difference 0.00033 is equivalent to \(\frac{3}{10000}\).

### Step 5: Match with the given choices
Looking at the answer choices:
- Option **D** gives \(\frac{3}{10000}\), which matches our calculation.

### Conclusion:
The correct answer is **D**: \(\frac{3}{10000}\).

---

Would you like further clarification on any step or have additional questions? Here are 5 related questions to deepen your understanding:

1. How do you convert a repeating decimal to a fraction?
2. Why is \(\frac{1}{3}\) different from 0.333 exactly?
3. What is the general process for finding the difference between two decimals?
4. Can you express 0.00033 as a fraction in another way?
5. How would the answer change if more decimal places were given for 0.3333?

**Tip:** When dealing with repeating decimals, remember that they can never be fully represented by a finite decimal, so be careful with rounding or truncating values!

What is the difference between one-third and 0.333?

Understand how to find the difference between one-third (a repeating decimal) and 0.333. Learn the steps involved in converting decimals to fractions and performing decimal subtraction, suitable for Grades 6-8.

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