Express 1400 ml as a percentage of 2.1 l. Solve it in detail.
The correct answer and explanation is:
To express 1400 ml as a percentage of 2.1 liters, we need to follow these steps:
Step 1: Convert units to the same scale
Since 1 liter = 1000 milliliters, we convert 2.1 liters to milliliters: 2.1 liters=2.1×1000=2100 ml2.1 \, \text{liters} = 2.1 \times 1000 = 2100 \, \text{ml}
Step 2: Use the percentage formula
Percentage=(PartWhole)×100\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
Here,
Part = 1400 ml,
Whole = 2100 ml Percentage=(14002100)×100\text{Percentage} = \left( \frac{1400}{2100} \right) \times 100 =(23)×100=66.6‾%= \left( \frac{2}{3} \right) \times 100 = 66.\overline{6}\%
✅ Final Answer: 1400 ml is approximately 66.67% of 2.1 liters.
📘 Detailed Explanation (300 words)
Understanding how to express a quantity as a percentage of another is an essential skill in mathematics, especially in real-world situations involving comparisons. In this case, the question asks us to express 1400 milliliters (ml) as a percentage of 2.1 liters (l).
The first step is to ensure both measurements are in the same unit. Since 1 liter is equal to 1000 milliliters, we convert 2.1 liters to milliliters: 2.1 l=2.1×1000=2100 ml2.1 \text{ l} = 2.1 \times 1000 = 2100 \text{ ml}
Now both values—1400 ml and 2100 ml—are in the same unit, making the comparison straightforward.
Next, we apply the percentage formula: Percentage=(PartWhole)×100\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
Substituting in the values: =(14002100)×100= \left( \frac{1400}{2100} \right) \times 100
Simplifying the fraction: 14002100=23\frac{1400}{2100} = \frac{2}{3}
Then multiplying by 100: 23×100=66.67%\frac{2}{3} \times 100 = 66.67\%
So, 1400 ml is approximately 66.67% of 2.1 liters. This method is widely used in problems involving proportions, recipes, liquid measurements, budgeting, and data analysis, where expressing one value as a part of another in percentage form provides a clearer and more interpretable picture.