Convert 250 cm3 to dm3 using only the equalities given. (1 mL = 1 cm3; 1 L = 1 dm3; milli = 10-3)
The Correct Answer and Explanation is:
To convert 250 cm³ to dm³, we can follow these steps:
Step 1: Understand the Equalities
- 1 mL = 1 cm³ (since 1 milliliter is equal to 1 cubic centimeter)
- 1 L = 1 dm³ (since 1 liter is equal to 1 cubic decimeter)
- milli = 10^-3 (which means 1 mL is 10^-3 L)
Step 2: Start from the Given Value
We are given 250 cm³. Since 1 cm³ is equivalent to 1 mL, we can directly convert 250 cm³ to mL:250 cm3=250 mL250 \, \text{cm}^3 = 250 \, \text{mL}250cm3=250mL
Step 3: Convert mL to L
We know that 1 mL is equal to 10^-3 L (1 mL = 10^-3 L). To convert 250 mL to liters, we multiply by 10^-3:250 mL×10−3=0.25 L250 \, \text{mL} \times 10^{-3} = 0.25 \, \text{L}250mL×10−3=0.25L
Step 4: Convert L to dm³
Since 1 L = 1 dm³ (1 liter is equal to 1 cubic decimeter), we can directly convert the result to dm³:0.25 L=0.25 dm30.25 \, \text{L} = 0.25 \, \text{dm}^30.25L=0.25dm3
Final Answer
Thus, 250 cm³ is equal to 0.25 dm³.
Explanation
In this problem, we used the fact that cubic centimeters (cm³) and milliliters (mL) are equivalent. Then, we used the conversion factor to convert mL to liters, and finally, since 1 liter is equal to 1 cubic decimeter (dm³), we obtained the final result of 0.25 dm³. This method ensures that all units are consistent with the given equalities.
