Question

Which conversion requires division? Use the metric table to help answer the question.

Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
kilograms to centigrams
decimeters to millimeters
hectometers to decimeters
decigrams to dekagrams

Answer 1

To determine which conversion requires division, we need to analyze each option based on the metric prefixes, which represent different powers of ten:

1. **Kilograms to Centigrams**:
- 1 kilogram (kg) = 1,000 grams (g).
- 1 gram (g) = 100 centigrams (cg).
- Therefore, 1 kg = 1,000 g = 100,000 cg.
- This conversion involves moving from a larger unit (kg) to a smaller unit (cg), which requires multiplication since we are increasing the number of units.

2. **Decimeters to Millimeters**:
- 1 decimeter (dm) = 10 centimeters (cm).
- 1 centimeter (cm) = 10 millimeters (mm).
- Therefore, 1 dm = 10 cm = 100 mm.
- This also involves moving from a larger unit (dm) to a smaller unit (mm), requiring multiplication as well.

3. **Hectometers to Decimeters**:
- 1 hectometer (hm) = 100 meters (m).
- 1 meter (m) = 10 decimeters (dm).
- Therefore, 1 hm = 100 m = 1,000 dm.
- This conversion involves moving from a larger unit (hm) to a smaller unit (dm), requiring multiplication.

4. **Decigrams to Dekagrams**:
- 1 decigram (dg) = 0.1 grams (g).
- 1 dekagram (dag) = 10 grams (g).
- Therefore, to convert from a smaller unit (dg) to a larger unit (dag), you will end up dividing (since 1 dg = 0.1 g, and you need to know how many dg are in 1 dag).

Among the options provided, the conversion that requires division is **decigrams to dekagrams**.