Which conversions involve multiplying by a positive power of 10? Select all that apply.

To determine which conversions involve multiplying by a positive power of 10, we can review each conversion step by step.

1. 6 kiloliters to centiliters:

   • 1 kiloliter = 1,000 liters
   • 1 liter = 100 centiliters Therefore, 1 kiloliter = 1,000 × 100 = 100,000 centiliters. Hence, multiplying by a positive power of 10.

2. 800 meters to hectometers:

   • 1 hectometer = 100 meters. To convert from meters to hectometers, we divide by 100 (which is the same as multiplying by \( \frac{1}{100} \)). Hence, this does not involve multiplying by a positive power of 10.

3. 0.8 dekameters to decimeters:

   • 1 dekameter = 10 meters, and 1 meter = 10 decimeters. Therefore, 1 dekameter = 10 × 10 = 100 decimeters. For 0.8 dekameters: \( 0.8 \times 100 = 80 \) decimeters. We are multiplying by 100 (which is \( 10^2 \)), hence this involves multiplying by a positive power of 10.

4. 13 hectograms to milligrams:

   • 1 hectogram = 100 grams, and 1 gram = 1,000 milligrams. Therefore, 1 hectogram = 100 × 1,000 = 100,000 milligrams. This is also multiplying by a positive power of 10.

Summary:

• Conversions that involve multiplying by a positive power of 10:
  • 6 kiloliters = ___ centiliters
  • 0.8 dekameters = ___ decimeters
  • 13 hectograms = ___ milligrams

So, the selected conversions are:

• 6 kiloliters = ___ centiliters
• 0.8 dekameters = ___ decimeters
• 13 hectograms = ___ milligrams