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Chapter 1: Problem 32

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

Short Answer

Expert verified
The sum of the distances is \(2134.66105 \mathrm{m}\).

Step by step solution

01

Convert Kilometers to Meters

To find the number of meters in \(2.13103 \mathrm{km}\), multiply the amount of kilometers by 1000 (as 1 kilometer equals 1000 meters): \(2.13103 \mathrm{km} * 1000 = 2131.03 \mathrm{m}\).
02

Sum up the distances

Now that both measurements are in the same units, they can be added together. So, \(3.63105 \mathrm{m} + 2131.03 \mathrm{m} = 2134.66105 \mathrm{m}\).

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Key Concepts

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

Addition of Lengths
When faced with a problem that involves adding lengths, it is crucial to ensure that all measurements are in the same unit before proceeding. This ensures accuracy and avoids confusion.
When units mismatch (like mixing meters and kilometers), converting one unit to match another is the first step.
Once both measurements share the same unit, simply sum them up like a traditional addition problem. This rule holds for any units such as inches, feet, yards, kilometers, or meters.
  • Avoid jumping straight to addition without first standardizing units.
  • Check your conversions before and after adding to avoid errors.
When the units match, the result is straightforward: add the numbers and maintain the unit in the result.
Kilometers to Meters Conversion
Converting kilometers to meters is a fundamental unit conversion skill. Kilometers and meters are both units of length in the metric system, with kilometers being the larger unit.
To convert, remember that a kilometer is simply 1000 times larger than a meter.
For instance, to convert 2.13103 kilometers to meters, multiply it by 1000:
  • Formula: \[ ext{Meters} = ext{Kilometers} \times 1000\]
  • Application: \[2.13103 ext{ kilometers} \times 1000 = 2131.03 ext{ meters}\]
Recognizing this conversion is essential because many practical problems involve switching between these two units. A quick check after converting will prevent errors and lead to precise measurements.
Distance Calculation
Distance calculation often combines concepts like unit conversion and addition of lengths. It's about finding total distances traveled or summing up segments.
Be sure to:
  • Convert any differing units to be consistent.
  • Add together the same unit measurements.
  • Review the final result for correctness.
Using the original exercise example, convert 2.13103 kilometers to meters before beginning your addition. Once conversion is complete, you can add the two distances: 3.63105 meters + 2131.03 meters.
The total distance then becomes 2134.66105 meters.
Double-check the math and units for a reliable answer. By understanding these foundational steps, you can tackle more complex problems as they arise in various mathematical applications.

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