Problem 35 - Prealgebra

Question

Set up the following problems as we have set up the examples in this section. Then use a calculator for the calculations and round your answers to the nearest hundredth. 49 qt to liters

Step-by-Step Solution

Answer

49 qt is approximately 46.36 liters.

Step 1: Understand the Conversion Factor

The conversion factor between quarts and liters is crucial for converting the units. You need to know that 1 quart is approximately equal to 0.946353 liters. This will be used to convert quarts to liters.

Step 2: Set Up the Conversion Equation

Using the conversion factor from Step 1, set up an equation to convert 49 quarts into liters. The equation becomes: \[ ext{Liters} = 49 imes 0.946353 \]

Step 3: Perform the Calculation

Calculate the product of 49 and 0.946353 using a calculator. Doing so, you get: \[ 49 imes 0.946353 = 46.364297 \]

Step 4: Round the Result

The problem asks to round the answer to the nearest hundredth. From 46.364297, rounded to the nearest hundredth, the result is 46.36 liters.

Key Concepts

Understanding Conversion Factors

A conversion factor is an essential tool in unit conversion problems. It helps in transforming the quantity measured in one unit to another by establishing a ratio between two units. Conversion factors are derived from the equivalence of two different units. For instance, when converting quarts to liters, a vital conversion factor is that 1 quart equals approximately 0.946353 liters. This means for every quart, you have about 0.946353 liters.

When working through unit conversions, remember the conversion factor allows for a seamless change from one measurement system to another. To convert, simply multiply the original quantity by the conversion factor to get the result in the desired unit. This method is not only efficient but also minimizes errors if applied correctly.

The Role of Liters in Conversions

Liters are a unit of volume in the metric system. They are often used for measuring liquid volumes and are widely recognized internationally because of their convenience and standardization. Understanding how to convert other units, like quarts, to liters is crucial, especially in scientific contexts or international settings where the metric system is predominant.

In our example, we are converting 49 quarts to liters. Knowing that 1 quart is roughly 0.946353 liters allows you to set up the conversion by multiplying 49 by this conversion factor. This simple multiplication gives you a result in liters, demonstrating how liters serve as a versatile bridge between different volume measurements.

Mastering the Art of Rounding Numbers

Rounding numbers makes them easier to work with, particularly when precision beyond a certain point is unnecessary. In the exercise provided, after converting quarts to liters, the result is a long decimal number: 46.364297. However, the requirement is to round it to the nearest hundredth for simplicity.

Here's how rounding works: focus on the digit in the place immediately greater than the place you wish to round to. If this digit is 5 or higher, round up the number in the desired place by one. If it's lower than 5, keep the number in the desired place unchanged. For example, in 46.364297, the third decimal digit is 4, so the number rounds to 46.36 when rounding to the nearest hundredth.

• Rounding enhances clarity and reduces complexity in representation.
• It helps turn detailed numerical results into a more digestible form.
• Mastering rounding is crucial for accuracy in everyday math and scientific calculations.