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Chapter 8: Problem 26

Complete. 5280 yd =________ mi

Short Answer

Expert verified
3 miles

Step by step solution

01

Understand the Conversion Factor

To convert yards to miles, you need to know the conversion factor. There are 1760 yards in a mile. Thus, 1 mile = 1760 yards.
02

Set Up the Conversion

You have 5280 yards which you need to convert to miles. Use the conversion factor from Step 1 to set up a proportion.
03

Perform the Calculation

Divide 5280 yards by the conversion factor (1760 yards per mile) to find the number of miles. \[ \text{Miles} = \frac{5280 \text{ yards}}{1760 \text{ yards/mile}} = 3 \text{ miles} \]

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Key Concepts

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

yards to miles conversion
Converting yards to miles is straightforward once you know the conversion factor. One mile equals 1760 yards.
For instance, if you have 5280 yards and want to convert it to miles, you would use this exact conversion factor.
Just divide the number of yards by 1760, and you will find your result in miles.
Using our example: \[ \text{Miles} = \frac{5280 \text{ yards}}{1760 \text{ yards/mile}} = 3 \text{ miles} \]
This simple conversion can be remembered easily and used for various lengths.
basic arithmetic
Basic arithmetic involves addition, subtraction, multiplication, and division.
When converting units, division is often used, as seen in our example with yards to miles.
Dividing 5280 yards by 1760 yards per mile, you get 3 miles. This is a clear use of basic arithmetic.
Mastering these simple operations will help you in many areas, including unit conversions.
dimensional analysis
Dimensional analysis, also known as factor-label method, helps in converting units by multiplying by conversion factors.
It ensures that the units you want to cancel out do so, leading you to the desired unit.
Using our example, we set up the conversion as follows: \[ \text{Miles} = \frac{5280 \text{ yards}}{1760 \text{ yards/mile}} \]
The 'yards' units cancel out, leaving you with miles.
Dimensional analysis is a crucial tool in mathematics and science for accurate calculations.
proportions in mathematics
Proportions are equations that state two ratios are equal.
They are especially helpful in solving unit conversions and scaling problems.
For our conversion, we set up a proportion where 1760 yards is to 1 mile as 5280 yards is to X miles: \[ \frac{1760 \text{ yards}}{1 \text{ mile}} = \frac{5280 \text{ yards}}{X \text{ miles}} \]
Solving this proportion will give us the value of X, which is 3 in this case.
Understanding proportions can simplify many mathematical tasks efficiently.

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