Problem 66 - 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 \(7,362\) fl oz to gallons.

Step-by-Step Solution

Answer

7,362 fl oz = 57.52 gallons.

Step 1: Understanding the Relationship

First, understand the relationship between fluid ounces and gallons. There are 128 fluid ounces in one gallon.

Step 2: Setting Up the Conversion

To convert from fluid ounces to gallons, divide the number of fluid ounces by the number of fluid ounces per gallon. Use the formula: \[\text{gallons} = \frac{\text{fluid ounces}}{128}\]

Step 3: Performing the Calculation

Substitute the given value into the formula: \[\text{gallons} = \frac{7,362}{128}\] Use a calculator to perform the division, which gives approximately 57.515625.

Step 4: Rounding the Result

Round the resulting number to two decimal places. The number 57.515625 rounds to 57.52 when rounded to the nearest hundredth.

Key Concepts

Fluid Ounces to Gallons

When converting fluid ounces to gallons, it's important to understand the relationship between these two units. In the United States, one gallon is equivalent to 128 fluid ounces. This is a foundational fact for performing conversions. You simply divide the number of fluid ounces by 128 to find out how many gallons you have.
For example, if you have 7,362 fluid ounces, you would use the equation:

• gallons = fluid ounces ÷ 128 = 7,362 ÷ 128

This straightforward division gives you the quantity in gallons. Understanding this relationship is key to performing the conversion accurately and effortlessly.

Division in Mathematics

Division is one of the fundamental operations in mathematics. It involves splitting a number into equal parts or groups. In essence, division helps us understand how many times one number is contained within another.
When converting units like fluid ounces to gallons, division is the chosen operation because you're determining how many units (fluid ounces) fit within a larger unit (gallon). The structure for performing division in this context is:

• Divide the total fluid ounces by the number of ounces in a gallon, using the formula: \[ \text{gallons} = \frac{\text{fluid ounces}}{128} \]

Being comfortable with division is essential for solving not just conversion problems but many mathematical problems efficiently.

Rounding Decimals

Rounding decimals is a common practice to simplify a number while maintaining its approximate value. Rounding involves reducing the number of digits after the decimal point. This process is especially useful in situations where precision beyond a certain point isn't necessary, or when a number must be reported in a more understandable form.
In this exercise, we round the result of our division, 57.515625, to two decimal places. This involves:

• Looking at the third decimal place (which is 5),
• Since it's 5 or more, we increase the second decimal by 1,
• The number becomes 57.52.

Rounding makes handling and interpreting numbers in practical situations much simpler.

Calculator Usage in Math

Calculators are indispensable tools in mathematics, providing quick and accurate calculations. When performing conversions or any arithmetic operations, a calculator can help avoid errors and save time.
To use a calculator for converting fluid ounces to gallons, follow these steps:

• Input the total number of fluid ounces, 7,362.
• Press the division operation key (÷).
• Input 128, the conversion factor from fluid ounces to gallons.
• Press the equals key (=) to get the result, which in this case is 57.515625.

Remember, although calculators are very helpful, they require you to understand the mathematical operations you're performing to ensure correct application and interpretation of results.