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Chapter 1: Problem 28

Add \(3.63105 \mathrm{m}\) and \(2.13103 \mathrm{km}\).

Short Answer

Expert verified
The sum of \(3.63105 \mathrm{m}\) and \(2.13103 \mathrm{km}\) is \(2134.66105 \mathrm{m}\).

Step by step solution

01

Convert Kilometers to Meters

First, convert the distance from kilometers to meters. Because we know that one kilometer equals 1000 meters, we multiply \(2.13103 \mathrm{km}\) by \(1000 \mathrm{m/km}\) to make the conversion: \(2.13103 \mathrm{km} * 1000 \mathrm{m/km} = 2131.03 \mathrm{m} \)
02

Add the Two Distances

Next, add the two distances together: \(3.63105 \mathrm{m} + 2131.03 \mathrm{m} = 2134.66105 \mathrm{m}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Meters and Kilometers
When we talk about measuring length or distance, we often use units such as meters and kilometers. These are part of the metric system, which is the standard system of measurement in most countries.
A meter, symbolized as "m," is a basic unit of length in the metric system. It's used for everyday measurements such as height or length of a room. The kilometer, symbolized as "km," is a larger unit and is often used to measure longer distances, like those between cities or the length of rivers.
A kilometer is equal to 1,000 meters. This conversion is crucial to make calculations simple so that different measurements can be easily compared or added together.
Remember:
  • 1 Kilometer = 1,000 Meters
  • Meters (m) are smaller than Kilometers (km)
  • For large distances, use kilometers; for smaller ones, use meters
Adding Measurements Together
In many practical situations, you might need to add together two measurements with different units. In our exercise, you need to add meters and kilometers.
Before adding, it's important to ensure that both measurements are in the same unit. This step avoids confusion and gives accurate results.
Here's how you can easily do it:
  • First, convert one of the measurements to the unit of the other. You can use the conversion fact that 1 km = 1,000 m to change kilometers to meters.
  • Once converted, simply add the measurements together. For example, if you have 3 meters and 2 kilometers, first convert the kilometers to 2,000 meters, then add the numbers to get 2,003 meters.
  • This process ensures accurate addition and makes it easier to handle various measurements in different units.
By following these steps, you'll be able to add measurements together quickly and correctly: just convert, and add.
The Basics of Measurement Conversion
Measurement conversion allows you to change a quantity expressed in one unit to another. This is especially handy when dealing with different units in calculations, like in our exercise with meters and kilometers.
The essence of conversion is using equivalent values 鈥� in our context, knowing that 1 km is equivalent to 1,000 m.
For accurate conversions:
  • Identify the conversion rate or factor between the units.
  • Multiply the original measurement by this factor if converting to a smaller unit (e.g., km to m).
  • If converting to a larger unit, you would divide instead (e.g., m to km). However, the exercise only deals with multiplying since converting km to m.
Employing these conversion strategies ensures that you can accurately and easily switch between units, avoiding calculation errors. Practicing these conversions can make you more proficient in solving various measurement problems.

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