Add the following rational numbers.
`3/10,0.4/100,(-21)/1000,7/10000`

Answer

To solve the problem of adding the rational numbers \( \frac{3}{10}, \frac{0.4}{100}, \frac{-21}{1000}, \frac{7}{10000} \), we will follow these steps:

### Step 1: Convert all numbers to have a common denominator
The denominators of the given numbers are 10, 100, 1000, and 10000. The least common denominator (LCD) is 10000.

### Step 2: Convert each rational number
1. **Convert \( \frac{3}{10} \)**:
\[ \frac{3}{10} = \frac{3 \times 1000}{10 \times 1000} = \frac{3000}{10000} \]

2. **Convert \( \frac{0.4}{100} \)**:
\[ 0.4 = \frac{4}{10} = \frac{4 \times 100}{10 \times 100} = \frac{40}{1000} = \frac{40 \times 10}{1000 \times 10} = \frac{400}{10000} \]

3. **Convert \( \frac{-21}{1000} \)**:
\[ \frac{-21}{1000} = \frac{-21 \times 10}{1000 \times 10} = \frac{-210}{10000} \]

4. **Convert \( \frac{7}{10000} \)**:
\[ \frac{7}{10000} \text{ (already in the correct form)} \]

### Step 3: Write all numbers with the common denominator
Now we have:
- \( \frac{3000}{10000} \)
- \( \frac{400}{10000} \)
- \( \frac{-210}{10000} \)
- \( \frac{7}{10000} \)

### Step 4: Add the numerators
Now we can add the numerators together:
\[ 3000 + 400 - 210 + 7 \]

Calculating step-by-step:
1. \( 3000 + 400 = 3400 \)
2. \( 3400 - 210 = 3190 \)
3. \( 3190 + 7 = 3197 \)

So, the sum of the numerators is \( 3197 \).

### Step 5: Write the final answer
Now we write the final answer as:
\[ \frac{3197}{10000} \]

### Step 6: Convert to decimal form (if needed)
To convert \( \frac{3197}{10000} \) to decimal:
\[ \frac{3197}{10000} = 0.3197 \]

Thus, the final answer is:
\[ \boxed{0.3197} \]