Problem 65 - Prealgebra

Question

Set up the following problems as you have been doing. Then use a calculator to perform the actual calculations. Round answers to two decimal places where appropriate. Convert 93.4 qt to gallons.

Step-by-Step Solution

Answer

93.4 quarts is 23.35 gallons.

Step 1: Understand the Relationship

To convert quarts to gallons, we need to know the conversion factor. There are 4 quarts in 1 gallon. This means 1 gallon equals 4 quarts.

Step 2: Set Up the Conversion Equation

Using the conversion factor, set up the equation to convert 93.4 quarts to gallons. This can be expressed as:\[ \text{gallons} = \frac{93.4}{4} \]

Step 3: Perform the Calculation

Divide 93.4 by 4 to get the equivalent amount in gallons. Using a calculator:\[ 93.4 \div 4 = 23.35 \]

Step 4: Round the Result

The calculated result, 23.35, is already rounded to two decimal places. Therefore, no further rounding is needed.

Key Concepts

Quarts to Gallons Conversion

Converting between different units of measurement is a common mathematical task. When turning quarts into gallons, it's important to understand their relationship. In this case, 1 gallon is equivalent to 4 quarts. This conversion factor is crucial. Whenever you need to convert quarts to gallons, just remember that you are essentially dividing the number of quarts by 4. For example, converting 93.4 quarts to gallons involves this simple calculation:

• Identify the number of quarts (in this instance, 93.4 quarts).
• Use the conversion factor: divide by 4 to find the number of gallons.
• Calculate: 93.4 divided by 4 equals the amount in gallons.

This straightforward equation will help you efficiently convert any quantity of quarts to gallons. Whether you're dealing with large portions or trying to understand recipes, knowing how to switch between these units is highly useful.

Rounding Decimals

Rounding decimals is a vital skill, especially when working with measurements or money. It simplifies numbers to make them easier to understand and use. The rule for rounding to two decimal places is particularly important, and here's how you do it.

• First, look at the number in the third decimal place. This is crucial because this number tells us what will happen to the second decimal place.
• If the third decimal place is 5 or greater, you'll round up the second decimal place. Otherwise, you leave it as is.
• For example, if you have 23.354, you only look at the 4 (third decimal place, which is less than 5), so 23.35 remains unchanged.

Rounding helps create neat, consistent figures, which are easier to read and interpret. It's a small detail that has a big impact on presenting accurate data.

Calculator Usage

Utilizing a calculator efficiently can significantly enhance your mathematical skills. Calculators aid in performing more complex calculations quickly, but they also require correct operation for accuracy. Calculators are user-friendly but here are some tips to make sure you're using them correctly:

• Always double-check the numbers you input. A small mistake in entering data can lead to incorrect results.
• Familiarize yourself with the basic functions. This includes addition, subtraction, multiplication, and division, which are often used.
• Remember to make use of the correct order of operations (PEMDAS/BODMAS) when computing equations that involve multiple steps.
• Finally, ensure your calculator is set to the correct mode. For rounding calculations, make sure to adjust it to show the desired decimal places.

By mastering these basic techniques, students can perform calculations more swiftly and with greater confidence.