Problem 5 - Prealgebra

Question

The distance between Tallahassee and Miami is 478 miles. Find the distance in kilometers if \(1 \mathrm{mi}=1.609 \mathrm{km} .\) Round to the nearest kilometer.

Step-by-Step Solution

Answer

The distance is 770 kilometers.

Step 1: Convert Miles to Kilometers

To find the distance in kilometers, multiply the given distance in miles by the conversion factor from miles to kilometers. Use the conversion rate: \(1 \text{ mile} = 1.609 \text{ km}\). So, the calculation will be: \( 478 \times 1.609 = 769.502 \text{ km} \).

Step 2: Round to the Nearest Kilometer

We need to round the resulting distance in kilometers from the previous step to the nearest whole number. Since we have \(769.502 \text{ km}\), and the first decimal is 5 (which is greater than or equal to 0.5), we round up to get \(770 \text{ km}\).

Key Concepts

Miles to Kilometers Conversion

Units of distance can vary based on the system used. In most of the world, the metric system is favored, which uses kilometers to measure distance. However, in the United States, miles are primarily used. Converting from miles (mi) to kilometers (km) is straightforward with a conversion factor. The accepted conversion is that one mile equals 1.609 kilometers.
To convert miles to kilometers:

• Multiply the number of miles by the conversion factor (1.609).
• For example, to convert 478 miles to kilometers, compute:

\[478 \times 1.609 = 769.502 \text{ km}\]Converting units this way helps in understanding and communicating distance measurements internationally.

Rounding Numbers

Rounding is the process of adjusting a number to make it simpler or to fit certain criteria, like to the nearest whole number. It's a vital skill in mathematical calculations where precision is less important or impractical.
Here's a simple guide to rounding a number:

• Identify the decimal place to which you want to round. In this example, we want to round to the nearest kilometer, or whole number.
• Look at the first digit to the right of your rounding place. If this digit is 5 or more, round up. If it's less than 5, round down.

For the distance conversion of 769.502 km:

• The first decimal is 5. As per the rules, this means rounding up, resulting in 770 km.

Rounding makes calculations cleaner and more understandable when extreme precision is not needed.

Distance Calculation

Calculating distance often requires the conversion between different units and sometimes involves rounding off numbers for simplicity. Whether you're traveling between two cities or calculating a route, understanding how to perform these calculations confidently is crucial.
Basic steps for distance calculation include:

• Determining the units of distance, such as miles or kilometers.
• Using appropriate conversion factors to switch units if necessary. In our case, converting miles to kilometers.
• Applying mathematical operations like multiplication for conversion and following up with rounding to get user-friendly results.

For example, when calculating the distance between Tallahassee and Miami:

• First, convert 478 miles using the conversion rate 1 mile = 1.609 km.
• This results in 769.502 km after multiplying.
• Rounding provides a tidy figure of 770 km for practical use.

Distance calculations ensure that you have a clear and understandable grasp of how far locations are from each other, which is particularly beneficial in travel planning and geography education.