An eye medication that is used to treat increased pressure inside the eye is packaged in 2.5 milliliter bottles. During the manufacturing process, a 10 decaliter capacity bin is used to fill the bottles. If1 decaliter is equivalent to 10 liters and 1 liter is equivalent to 1,000 milliliters, what is the maximum number of bottles that can be filled?

Options

A. `4times10^(5)`
B. `4times10^(4)`
C. `2.5times10^(3)`
D. `2.5times10^(2)`

Answer

To solve the problem of how many 2.5 milliliter bottles can be filled from a 10 decaliter capacity bin, we will follow these steps:

### Step 1: Convert Decaliters to Liters
We know that:
1 decaliter = 10 liters

Given that the bin has a capacity of 10 decaliters, we can convert this to liters:
\[ \text{Capacity in liters} = 10 \text{ decaliters} \times 10 \text{ liters/decaliter} = 100 \text{ liters} \]

### Step 2: Convert Liters to Milliliters
Next, we convert liters to milliliters. We know that:
1 liter = 1000 milliliters

Thus, we convert the 100 liters to milliliters:
\[ \text{Capacity in milliliters} = 100 \text{ liters} \times 1000 \text{ milliliters/liter} = 100000 \text{ milliliters} \]

### Step 3: Calculate the Number of Bottles
Now that we have the total capacity in milliliters, we can find out how many 2.5 milliliter bottles can be filled:
\[ \text{Number of bottles} = \frac{\text{Capacity of bin in milliliters}}{\text{Capacity of one bottle in milliliters}} = \frac{100000 \text{ milliliters}}{2.5 \text{ milliliters/bottle}} \]

### Step 4: Perform the Division
Now we perform the division:
\[ \text{Number of bottles} = \frac{100000}{2.5} = 40000 \]

### Final Answer
The maximum number of bottles that can be filled is **40000**.

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