Problem 37 - Algebra 1: Concepts and Skills

Question

In Exercises \(32-37\), convert the units. Round the result to the nearest tenth. 2000 meters to kilometers (1 kilometer \(=1000\) meters)

Step-by-Step Solution

Answer

The converted value is 2 kilometers.

Step 1: Understand the conversion rate

The problem provides us the conversion rate needed for the problem which is 1 kilometer is equal to 1000 meters.

Step 2: Perform the Conversion

Take the given value in meters and divide it by the value of kilometers. Hence, \[2000 / 1000 = 2\] kilometers.

Key Concepts

Meters to Kilometers

When converting meters to kilometers, understanding the basic relationship between these units of length is crucial. Both meters and kilometers are part of the metric system, which makes conversion relatively simple. The metric system is decimal-based, meaning it uses base 10 for its conversions. Therefore, when converting from meters to kilometers, you're essentially shifting the decimal place over to the left by three places.

You have 1000 meters in a kilometer. Thus, if you have a distance of 2000 meters, you'd divide by 1000 to find out how many kilometers this distance equals. Mathematically, you would perform this calculation as follows:

\( \frac{2000 \text{ meters}}{1000} \) which equals 2 kilometers.

This is a direct and straightforward process thanks to the simplicity of the metric system's design.

Conversion Rate

A conversion rate is a crucial factor to understand when converting one unit of measurement to another. It acts as a standard or reference point that tells you how many of one unit are equal to another. In this particular case, the conversion rate is 1 kilometer equaling 1000 meters.

This import ratio allows you to easily switch from measuring in meters to kilometers or vice versa. By dividing the number of meters by 1000, you are essentially converting your measurement into kilometers because this rate tells you how many smaller units make up the larger unit.

Understanding conversion rates like this one can save time and prevent errors in calculations, especially when working with systems that use similar-sized units, such as the metric system.

Rounding to the Nearest Tenth

When solving problems that involve calculations, especially conversions, it's often necessary to round your results. In this problem, we are asked to round our answer to the nearest tenth. Rounding rules help you present your answer in a more manageable or precise form.

To round a number to the nearest tenth, look at the digit in the hundredths place (the second digit to the right of the decimal point). If this digit is 5 or more, increase the tenths digit (the first digit to the right of the decimal point) by one. If it's less than 5, you leave the tenths digit as it is.

For instance, if your result was 2.47 kilometers, you would look at the 7. Since 7 is more than 5, you would round the decimal up to the nearest tenth to get 2.5 kilometers. This step ensures your answer is both accurate and neatly presented.