Problem 53 - Prealgebra

Question

Set up the following conversions as you have been doing. Then perform the calculations on a calculator. Mount Whitney is the highest point in California. It is \(14,494\) feet above sea level. Give its height in miles to the nearest tenth.

Step-by-Step Solution

Answer

Mount Whitney is approximately 2.7 miles above sea level.

Step 1: Understanding the Problem

We need to convert Mount Whitney's height from feet to miles. We know Mount Whitney is 14,494 feet above sea level, and we need to find out how many miles this is, rounded to the nearest tenth.

Step 2: Unit Conversion Factor

1 mile is equivalent to 5,280 feet. This is our unit conversion factor which we will use to convert feet into miles.

Step 3: Set Up the Conversion

To convert feet to miles, set up the conversion as follows: \(14,494 \text{ feet} \times \frac{1 \text{ mile}}{5,280 \text{ feet}}\). This equation sets up a conversion where 'feet' units will cancel out, leaving us with 'miles'.

Step 4: Perform the Calculation

Calculate the conversion by performing the division: \(\frac{14,494}{5,280}\). By using a calculator, this division gives us approximately 2.7447 miles.

Step 5: Round the Result

Round the result to the nearest tenth as the problem requests. The value 2.7447 rounded to the nearest tenth is 2.7.

Key Concepts

Feet to Miles Conversion

Feet to miles conversion is an essential skill, especially when dealing with large distances. It's commonly used in areas like geography, travel, and science. Mount Whitney, for example, is 14,494 feet above sea level, and converting this height into miles helps better visualize its size compared to other metric scales. To convert feet to miles, remember that 1 mile is equal to 5,280 feet. This constant, the unit conversion factor, allows you to perform the conversion. Simply multiply the number of feet by the fraction \(\frac{1 \text{ mile}}{5,280 \text{ feet}}\). This operation will cancel the 'feet' units and leave you with the distance in miles.

Rounding Numbers

Rounding numbers is an important mathematical concept used to simplify numbers for easier interpretation. In the context of Mount Whitney's height, after converting from feet to miles, you end up with a figure like 2.7447 miles. Such a specific number might be hard to use in everyday scenarios. Therefore, you might round this number to make it easier to understand:

• Identify the place to which you need to round (nearest tenth, hundredth, etc.).
• Look at the digit directly to the right of the designated place.
• If this digit is 5 or greater, round up the designated place by one. Otherwise, round down.

So, rounding 2.7447 to the nearest tenth means you look at the digit in the hundredths place, which is 4. Since it's less than 5, the result is rounded to 2.7.

Using a Calculator for Conversions

Using a calculator efficiently for conversions helps with precision and saves time. When converting between units like feet and miles, manual calculations can become cumbersome, especially with large numbers or detailed operations. Here's how a calculator helps in converting 14,494 feet to miles:

• First, know your conversion factor: 5,280 feet = 1 mile.
• Then, divide the number of feet (14,494) by 5,280 to get the result in miles.
• Use your calculator to perform the division. Input the expression \(\frac{14,494}{5,280}\) to get approximately 2.7447 miles.

Calculators enhance accuracy and prevent the common pitfalls of manual calculations, like arithmetic errors. Therefore, they're invaluable tools in both academic and real-world applications.