Question

Which conversions involve multiplying by a positive power of 10? Select all that apply.
6 kiloliters = ___ centiliters
800 meters = ___ hectometers
0.8 dekameters = ___ decimeters
13 hectograms = ___ milligrams
A 2-column table with 7 rows. Column 1 has entries kilo, hecto, deka, unit, deci, centi, milli. Column 2 has entries 1,000, 100, 10, 1, 0.1, 0.01, 0.001.

Answer 1

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