Problem 48 - Prealgebra

Question

Make the following conversions using the conversion factors given in Tables 3 and 4 \(4.71 \mathrm{kL}\) to liters

Step-by-Step Solution

Answer

4.71 kL is equivalent to 4710 liters.

Step 1: Understand the Conversion Factor

The problem requires converting kiloliters (kL) to liters (L). According to conversion tables, 1 kiloliter is equivalent to 1000 liters. That is, \(1 \text{kL} = 1000 \text{L}\).

Step 2: Set Up the Conversion Equation

To convert 4.71 kiloliters to liters, use the conversion factor from Step 1. Multiply the number of kiloliters by the conversion factor: \(4.71 \text{kL} \times 1000 \text{L/kL}\).

Step 3: Perform the Calculation

Carry out the multiplication: \(4.71 \times 1000 = 4710\). So, \(4.71 \text{kL} = 4710 \text{L}\).

Key Concepts

Understanding Kiloliters to Liters Conversion

Converting from kiloliters (kL) to liters (L) is an essential metric conversion that is quite common in various fields, especially when dealing with volumes of liquids. The metric system is structured to make these conversions simple. In particular, the base unit for volume is the liter, and the kiloliter is a larger unit.
To understand the conversion from kiloliters to liters, it's helpful to think of the prefix "kilo-" which means 1000. So, 1 kiloliter is equivalent to 1000 liters.

• 1 kiloliter (kL) = 1000 liters (L)

This simple relationship allows you to convert any amount measured in kiloliters to liters with straightforward multiplication by 1000.
When faced with a real-world example such as converting 4.71 kL to liters, you would multiply 4.71 by 1000, resulting in 4710 liters. This allows for easy calculation and ensures precision in handling large volumes of liquid.

The Role of Conversion Factors

A conversion factor is a critical tool in unit conversions, like turning kiloliters into liters. This factor allows us to change the unit of a measurement while keeping the quantity equivalent. Conversion factors are derived from known relationships between units.
In our case of converting kiloliters to liters, the conversion factor is 1000 because 1 kiloliter is equal to 1000 liters.

• This means the conversion factor formula is: \[ 1 \text{kL} = 1000 \text{L}\]

By using a conversion factor, you can systematically convert between units without changing the measurement's value. You multiply the quantity by the conversion factor, aligning the units so they cancel out or switch as needed. In the example with 4.71 kiloliters, multiplying by 1000 (the conversion factor) directly translates the measurement into liters.

Applying Prealgebra in Unit Conversions

Prealgebra provides the foundational skills needed for understanding and performing unit conversions. It revolves around basic arithmetic such as multiplication and the manipulation of equations. These skills are crucial when using conversion factors.
Consider the conversion from kiloliters to liters as a straightforward problem of multiplying a number by 1000. This requires a good grasp of multiplication, which is a key component of prealgebra.

• Set up the equation: \[ 4.71 \text{kL} \times 1000 \text{L/kL} = 4710 \text{L}\]
• Performing the multiplication results in the conversion.

Understanding how to manipulate numbers and equations is central in prealgebra. It ensures success in units conversion, especially in scientific contexts where precision is key. Converting units like kiloliters to liters is one of many practical applications of prealgebra skills.