Which of the following unit conversions is wrong?

Options

A. 1 km = `10^9 mu m`
B. 1 cm = `10^3` mm
C. 1 mg = `10^3 mu g`
D. 1 kg = `10^6` mg

Explanation

To determine which unit conversion is wrong, we will analyze each option step by step.

### Step 1: Analyze Option 1
**Conversion:** 1 km = 10^9 micrometers

1. **Convert kilometers to meters:**
- 1 km = 1000 meters = 10^3 meters.

2. **Convert meters to micrometers:**
- 1 meter = 10^6 micrometers.

3. **Combine the conversions:**
- 1 km = 10^3 meters = 10^3 * 10^6 micrometers = 10^(3+6) micrometers = 10^9 micrometers.

**Conclusion:** This conversion is correct.

### Step 2: Analyze Option 2
**Conversion:** 1 cm = 10^3 mm

1. **Convert centimeters to meters:**
- 1 cm = 0.01 meters = 10^-2 meters.

2. **Convert meters to millimeters:**
- 1 meter = 1000 mm = 10^3 mm.

3. **Combine the conversions:**
- 1 cm = 10^-2 meters = 10^-2 * 10^3 mm = 10^(3-2) mm = 10^1 mm = 10 mm.

**Conclusion:** This conversion is incorrect. It should be 1 cm = 10 mm, not 10^3 mm.

### Step 3: Analyze Option 3
**Conversion:** 1 mg = 10^3 micrograms

1. **Convert milligrams to grams:**
- 1 mg = 10^-3 grams.

2. **Convert grams to micrograms:**
- 1 gram = 10^6 micrograms.

3. **Combine the conversions:**
- 1 mg = 10^-3 grams = 10^-3 * 10^6 micrograms = 10^(6-3) micrograms = 10^3 micrograms.

**Conclusion:** This conversion is correct.

### Step 4: Analyze Option 4
**Conversion:** 1 kg = 10^6 mg

1. **Convert kilograms to grams:**
- 1 kg = 1000 grams = 10^3 grams.

2. **Convert grams to milligrams:**
- 1 gram = 1000 mg = 10^3 mg.

3. **Combine the conversions:**
- 1 kg = 10^3 grams = 10^3 * 10^3 mg = 10^(3+3) mg = 10^6 mg.

**Conclusion:** This conversion is correct.

### Final Conclusion
The wrong unit conversion is in **Option 2**: 1 cm = 10^3 mm is incorrect; it should be 1 cm = 10 mm.

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