Question

An airplane is cruising at a specd of 785 miles per hour. Convert this speed to kilometers per hour.

Short answer

The airplane's cruising speed is approximately 1263.3339 kilometers per hour.

Step-by-step solution

Understand the Conversion Factor

To convert miles to kilometers, use the conversion factor where 1 mile is approximately equivalent to 1.60934 kilometers.

Set Up the Conversion Equation

Multiply the cruising speed of the airplane in miles per hour by the conversion factor to obtain the speed in kilometers per hour.

Perform the Conversion

Calculate the speed in kilometers per hour by multiplying 785 miles per hour by 1.60934.

Calculate and Find the Answer

785 miles/hour * 1.60934 = 1263.3339 kilometers/hour. The speed of the airplane in kilometers per hour is approximately 1263.3339 km/h.

Key concepts

Miles to Kilometers Conversion

Understanding how to convert miles to kilometers is a fundamental skill in mathematics, especially in situations involving distances or speeds. For example, in the exercise provided, an airplane cruising speed of 785 miles per hour needs to be converted to kilometers per hour.

Why do we need to convert? The answer is simple: different regions use different units of measurement. While the United States commonly uses miles, most other countries use kilometers. Converting between these units allows for a better understanding of speed or distance in a universal context.

To convert miles to kilometers, you always use the same conversion factor. One mile is approximately equivalent to 1.60934 kilometers. So, to convert any distance or speed from miles to kilometers, you would multiply the number of miles by this factor.

It's always best to keep the conversion factor handy or memorize it for quick calculations when needed. Regardless of the context, whether it's an airplane's speed or the distance of a road trip, the process of conversion remains consistent.

Mathematical Conversion Factors

Conversion factors are the backbone of unit conversion problems in mathematics. They are the special numbers that allow you to convert one unit into another. In essence, a conversion factor is a form of equivalence statement between two units. For instance, the conversion factor for miles to kilometers, as previously mentioned, is 1.60934.

When dealing with conversion factors, it is important to always verify their accuracy. Using an incorrect conversion factor can lead to significant mistakes in calculations. Factors can be found in mathematics textbooks, reliable online resources, or even on measuring instruments themselves.

Creating a Conversion Factor

Notably, a conversion factor can be flipped and used the other way around as well. If you know the conversion from miles to kilometers, you automatically know the conversion from kilometers to miles; just divide 1 by the conversion factor (1 / 1.60934).

Conversion factors are not limited to just distance or speed conversions; they apply to any type of unit conversion including volume, weight, and temperature. Appropriate use of conversion factors in calculations is essential for obtaining correct results.

Multiplication in Unit Conversion

In unit conversion, multiplication is used to transform a quantity from one set of units to another set of units using a conversion factor. This step is key in ensuring that the dimensions of the measurement are maintained while changing the 'scale' of the units involved.

To perform a multiplication for unit conversion, you follow these general steps:

• Identify the correct conversion factor.
• Set up the equation by placing the quantity to be converted on one side and the conversion factor on the other.
• Multiply the original quantity by the conversion factor.
• If necessary, perform repeat conversions (multiply by another conversion factor) until the desired unit is achieved.

In our exercise, we multiply 785 miles/hour by the conversion factor of 1.60934 to convert the speed to kilometers per hour. Through this multiplication process, we maintain the aspect of speed (distance over time) while converting from the customary units used in the U.S. to the metric units recognized internationally.

It's also crucial to ensure that units are correctly canceled out during multiplication. In our example, since we wanted to convert 'miles' to 'kilometers', after multiplication, 'miles' units cancel out, leaving us with the desired 'kilometers'. Getting comfortable with the multiplication aspect of unit conversion can greatly enhance one's proficiency in a wide array of mathematical and scientific computations.