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Chapter 8: Problem 20

\(1862 \mathrm{mi}=\)___________ \(\mathrm{km}\) (The distance from Seattle to Kansas City)

Short Answer

Expert verified
1862 mi = 2997.50 km

Step by step solution

01

Identify the Conversion Factor

To convert miles to kilometers, use the conversion factor: 1 mile = 1.60934 kilometers.
02

Set Up the Conversion Equation

Multiply the given distance in miles by the conversion factor to find the distance in kilometers: \(1862 \text{ mi} \times 1.60934 \text{ km/mi}\).
03

Perform the Multiplication

Calculate the multiplication: \(1862 \times 1.60934 = 2997.49708\).
04

Round the Result

Round the result to an appropriate number of decimal places, usually two: \(2997.50\) kilometers.

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Key Concepts

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

miles to kilometers
Converting from miles to kilometers is a common task in many areas, such as travel planning and scientific measurements. The main idea is to change the unit of measurement from miles (a unit commonly used in the United States) to kilometers (used in most other countries and in scientific contexts). Understanding the conversion process ensures that distances are accurately reported, regardless of the unit used. This is particularly useful when comparing distances or planning trips that involve different measurement systems.
conversion factor
The conversion factor is a number used to change one set of units to another, by multiplying or dividing. In our case, to convert miles to kilometers, you use the conversion factor of 1.60934. This means that 1 mile equals 1.60934 kilometers. It's crucial to remember this value as it acts as the bridge between the two units.

Here is how you use it:
  • Identify the distance in miles that you need to convert
  • Multiply that distance by the conversion factor (1.60934 km/mi)
This will give you the equivalent distance in kilometers.
multiplication
Multiplication is the mathematical process used to calculate the new distance in kilometers. You simply take the number of miles and multiply it by the conversion factor. For example, if the distance is 1862 miles, you multiply 1862 by 1.60934.

The formula in LaTeX is: \( \text{Distance in km} = \text{Distance in mi} \times 1.60934 \)
Perform the multiplication as demonstrated:
\( 1862 \text{ mi} \times 1.60934 \text{ km/mi} = 2997.49708 \text{ km} \).
This step ensures you get an accurate result before rounding.
rounding decimals
Rounding decimals is the process of trimming down a long decimal number to a more convenient and readable form. It鈥檚 especially useful in making the final result easier to report and understand, without significantly affecting accuracy.

In our example, after calculating the multiplication, we get 2997.49708 kilometers.
  • Decide how many decimal places you need (usually two is sufficient in most practical cases)
  • Round the number accordingly: \(2997.49708 \rightarrow 2997.50 \)
This makes the result 2997.50 km, which is easier to read and use.

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Most popular questions from this chapter

Convert to Celsius. Use the formula \(C=\frac{5}{9} \cdot(F-32)\) or \(C=\frac{F-32}{1.8}\). $$ \begin{aligned} &98.6^{\circ} \mathrm{F}\\\ &\text { (Normal body temperature) } \end{aligned} $$

Complete. 1 wk =______days

Convert to Fahrenheit. Use the formula \(F=\frac{9}{5} \cdot C+32\) or \(F=1.8 \cdot C+32\). $$ 90^{\circ} \mathrm{C} $$

The biblical measure called a span was considered to be half of a cubit \((1\) cubit \(\approx 18\) in. see Exercise 47 ). The giant Goliath's height "was six cubits and a span" (Holy Bible, King James Version, 1 Sam. 17: 4 ). What was the height of Goliath in inches? in feet?

Solve. $$ 1.95 \cdot w=0.078 $$
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