Problem 53 - Prealgebra

Question

Since the pilot of a hot air balloon can only control the balloon's altitude, he relies on the winds for travel. To ride on the jet streams, a hot air balloon must rise as high as 12 kilometers. Convert this to miles by dividing by 1.61. Round your answer to the nearest tenth of a mile.

Step-by-Step Solution

Answer

12 kilometers is approximately 7.5 miles.

Step 1: Understand the Problem

We need to convert 12 kilometers to miles. The conversion rate is 1 kilometer = 1.61 miles. We will divide the given kilometers by 1.61 to find the distance in miles.

Step 2: Set Up the Conversion Equation

Using the conversion factor, we write the equation to convert kilometers to miles: \( D_{miles} = \frac{12 \text{ km}}{1.61} \).

Step 3: Perform the Division

Calculate the division to find the miles: \( \frac{12}{1.61} \approx 7.453 \) miles.

Step 4: Round the Result

The problem asks for an answer rounded to the nearest tenth. So, we round 7.453 to 7.5 miles.

Key Concepts

Kilometers to Miles Conversion

Converting between kilometers and miles is an important skill in various contexts like travel and geography. Kilometers and miles are units used to measure distance. While kilometers are part of the metric system, miles belong to the imperial system. To convert kilometers to miles, you need a conversion factor. This is a number you use to switch from one unit to another. Here, 1 kilometer is approximately 0.6214 miles. However, in many exercises, you might see a simplified conversion factor of 1.61.

• Step 1: Identify the conversion rate. For kilometers to miles, the conversion factor given in this exercise is 1 kilometer = 1.61 miles.
• Step 2: Convert the distance. If you have a distance in kilometers, you divide that number by 1.61 to get the distance in miles.

Understanding how to use conversion factors will make it possible to switch between different units of measurement easily.

Understanding Distance Measurement

Distance measurement is crucial for navigation, mapping, and everyday calculations. Distances can be expressed in various units, depending on geographic location and preferences. In the United States, miles are more commonly used, while the rest of the world typically uses kilometers.

• Distance refers to the length between two points. In this exercise, it’s the height a hot air balloon must travel.
• Knowing the difference in kilometers and miles helps you better plan and understand routes or trips.

Using familiar units makes understanding and communication easier, especially in transportation or international contexts.

Rounding Numbers

Rounding numbers is all about making them simpler while keeping them close to what they were. It’s often used to make numbers easier to work with or understand.

• To round a number to the nearest tenth, look at the number in the hundredths place.
• If the number is 5 or greater, round up. If it's less, round down.

For example, when you have 7.453 miles and need to round to the nearest tenth, you check the hundredths place, which is 5. Since it’s 5, you’d round up, resulting in 7.5 miles. Thus, rounding helps in achieving results that are simple to communicate and often adequate for practical purposes.