To find the largest amount in each box, we need to convert all units to a common base for comparison. Let's do that step-by-step for each category.
### 1. Weight (first box):
- 200 kg is [tex]\(200 \times 1000 = 200,000\)[/tex] grams.
- 20 g is already in grams.
- 20 dag (decagrams) is [tex]\(20 \times 10 = 200\)[/tex] grams.
The largest amount is 200,000 grams (200 kg).
### 2. Volume (second box):
- 4 L (liters) is [tex]\(4 \times 1000 = 4,000\)[/tex] milliliters.
- 2039 mL is already in milliliters.
- 860 mL is already in milliliters.
The largest amount is 4,000 milliliters (4 L).
### 3. Length (third box):
- 200 m is already in meters.
- 109 cm (centimeters) is [tex]\(109 / 100 = 1.09\)[/tex] meters.
- 20 dam (decameters) is [tex]\(20 \times 10 = 200\)[/tex] meters.
The largest amount is 200 meters (200 m).
### 4. Distance (fourth box):
- 13 km (kilometers) is [tex]\(13 \times 1000 = 13,000\)[/tex] meters.
- 290 m is already in meters.
- 29 hm (hectometers) is [tex]\(29 \times 100 = 2,900\)[/tex] meters.
The largest amount is 13,000 meters (13 km).
### 5. Small Weight (fifth box):
- 100 g is already in grams.
- 800 kg is [tex]\(800 \times 1000 = 800,000\)[/tex] grams.
- 1000 mg (milligrams) is [tex]\(1000 / 1000 = 1\)[/tex] gram.
The largest amount is 800,000 grams (800 kg).
Here is the table with the largest amounts circled in each box:
\begin{tabular}{|c|c|c|c|c|}
\hline [tex]\(\mathbf{200 \, kg}\)[/tex] & [tex]\(\mathbf{4 \, L}\)[/tex] & [tex]\(\mathbf{200 \, m}\)[/tex] & [tex]\(\mathbf{13 \, km}\)[/tex] & [tex]\(\mathbf{800 \, kg}\)[/tex] \\
20 g & 2039 mL & 109 cm & 290 m & 100 g \\
20 dag & 860 mL & 20 dam & 29 hm & 1000 mg \\
\hline
\end{tabular}
This identifies the largest quantity in each category based on the converted units for comparison.
