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Chapter 6: Problem 19

Change 25,756 feet to miles. Round your answer to the nearest tenth of a mile.

Short Answer

Expert verified
25,756 feet is approximately 4.9 miles when rounded to the nearest tenth.

Step by step solution

01

Understand the Conversion Factor

To convert feet to miles, we need to know the conversion factor between these units. 1 mile is equivalent to 5,280 feet.
02

Set Up the Conversion Equation

Use the conversion factor to set up an equation. You have 25,756 feet and want to find out how many miles that equates to. The equation is:\[\text{miles} = \frac{25,756 \text{ feet}}{5,280 \text{ feet/mile}}.\]
03

Perform the Division

Now, divide 25,756 by 5,280 to convert the measurement from feet to miles:\[\text{miles} = \frac{25,756}{5,280} \approx 4.87954.\]
04

Round the Result

The question asks to round the answer to the nearest tenth of a mile. Looking at the decimal 4.87954, the tenths place is 8, and the number following it is 7, indicating we round up. Therefore, 4.87954 rounds to 4.9.

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Key Concepts

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

Conversion Factor
In the realm of unit conversion, understanding conversion factors is crucial. A conversion factor is like a bridge that allows you to translate measurements from one unit to another. It鈥檚 a fixed number used to change units without altering the value of the original measurement.
For example, when converting feet to miles, the conversion factor is 5,280 feet per mile. This number means that for every mile, there are 5,280 feet.
  • To convert a measurement, you multiply by the conversion factor if you鈥檙e going to a larger unit (like feet to miles) or divide by it if going to a smaller unit.
  • Always ensure your units cancel out correctly, leaving you with the desired unit in your final result.
When you have a clear understanding of conversion factors, any unit conversion becomes a simple task of multiplication or division, as required by the specific problem.
Division
When you've set up your conversion equation, division is typically the mathematical operation needed to proceed. For the exercise of converting 25,756 feet to miles, this means dividing the number of feet by the conversion factor of 5,280 feet per mile.
The formula is straightforward: \[ \text{miles} = \frac{\text{total feet}}{5,280} \]
Substituting the exercise's values in gives:\[ \text{miles} = \frac{25,756}{5,280} \approx 4.87954 \]
  • This result tells us how many miles are in 25,756 feet.
  • Always ensure your division is precise to maintain accuracy before any additional rounding.
Division is your final step in changing measurements, converting the base unit into its larger or smaller counterpart.
Measurement Rounding
In most practical situations, particularly in math, converting large numbers might result in long decimals. This is where rounding becomes important. Rounding helps to simplify the number while still staying close to its true value, making it easier to interpret or report.
Based on the problem, you are asked to round to the nearest tenth. The original decimal after conversion was 4.87954.
  • Check the number at the hundredths place to determine how to round the tenths place.
  • If the hundredths digit (7 in this case) is 5 or more, you round the tenths place up.
Thus, 4.87954 becomes 4.9 after rounding.
Stay mindful of rounding rules as they ensure clarity, precision, and correctness in reporting your final answer.

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