The Actual Height of the Book

Oct 13, 2025 by vinooalluri.com 117 views

Introduction

In mathematics, estimating the height of an object is a common task that requires precision and accuracy. In this article, we will discuss the actual height of a book and Beverly's estimated height, and determine the range of values that represents her estimated height.

The Actual Height of the Book

The actual height of a book is given as $$9 \frac1}{4}$$ inches. This can be converted to a decimal by dividing the numerator by the denominator $$\frac{1{4} = 0.25$$. Therefore, the actual height of the book is $$9 + 0.25 = 9.25$$ inches.

Beverly's Estimated Height

Beverly estimates the height of the book and finds her percent error to be less than $$4%$$. This means that her estimated height is within $$4%$$ of the actual height. To find the range of values that represents her estimated height, we need to calculate the lower and upper bounds of her estimate.

Calculating the Lower Bound

The lower bound of Beverly's estimate is the actual height minus $$4%$$ of the actual height. To calculate this, we need to find $$4%$$ of the actual height and subtract it from the actual height.

4\%$$ of the actual height is calculated as follows:

0.04 \times 9.25 = 0.37 </span></p> <p>Therefore, the lower bound of Beverly's estimate is:</p> <p class='katex-block'><span class="katex-error" title="ParseError: KaTeX parse error: Can&#x27;t use function &#x27;$&#x27; in math mode at position 19: …5 - 0.37 = 8.88$̲$ inches ## Ca…" style="color:#cc0000">9.25 - 0.37 = 8.88$$ inches ## Calculating the Upper Bound The upper bound of Beverly&#x27;s estimate is the actual height plus $$4\%$$ of the actual height. To calculate this, we need to find $$4\%$$ of the actual height and add it to the actual height. $$4\%$$ of the actual height is calculated as follows: $$0.04 \times 9.25 = 0.37 </span></p> <p>Therefore, the upper bound of Beverly's estimate is:</p> <p class='katex-block'><span class="katex-error" title="ParseError: KaTeX parse error: Can&#x27;t use function &#x27;$&#x27; in math mode at position 19: …5 + 0.37 = 9.62$̲$ inches ## Th…" style="color:#cc0000">9.25 + 0.37 = 9.62$$ inches ## The Range of Values The range of values that represents Beverly&#x27;s estimated height is between the lower and upper bounds calculated above. Therefore, the range of values is: $$8.88 \leq \text{Estimated Height} \leq 9.62$$ inches ## Conclusion In this article, we discussed the actual height of a book and Beverly&#x27;s estimated height. We calculated the lower and upper bounds of her estimate and determined the range of values that represents her estimated height. The range of values is between $$8.88$$ and $$9.62$$ inches. ## Frequently Asked Questions * What is the actual height of the book? The actual height of the book is $$9 \frac{1}{4}$$ inches, which is equivalent to $$9.25$$ inches. * What is Beverly&#x27;s percent error? Beverly&#x27;s percent error is less than $$4\%$$. * What is the range of values that represents Beverly&#x27;s estimated height? The range of values that represents Beverly&#x27;s estimated height is between $$8.88$$ and $$9.62$$ inches. ## References * [1] &quot;Percent Error.&quot; Math Is Fun, mathisfun.com/percentage/percent-error.html. * [2] &quot;Estimating the Height of an Object.&quot; Math Open Reference, mathopenref.com/estimatingheight.html. ## Related Articles * [1] &quot;The Importance of Estimation in Mathematics.&quot; * [2] &quot;How to Calculate Percent Error.&quot; * [3] &quot;The Role of Estimation in Real-World Applications.&quot;&lt;br/&gt; # Q&amp;A: The Actual Height of a Book and Beverly&#x27;s Estimated Height ## Introduction In our previous article, we discussed the actual height of a book and Beverly&#x27;s estimated height. We calculated the lower and upper bounds of her estimate and determined the range of values that represents her estimated height. In this article, we will answer some frequently asked questions related to the topic. ## Q&amp;A ### Q1: What is the actual height of the book? A1: The actual height of the book is $$9 \frac{1}{4}$$ inches, which is equivalent to $$9.25$$ inches. ### Q2: What is Beverly&#x27;s percent error? A2: Beverly&#x27;s percent error is less than $$4\%$$. ### Q3: What is the range of values that represents Beverly&#x27;s estimated height? A3: The range of values that represents Beverly&#x27;s estimated height is between $$8.88$$ and $$9.62$$ inches. ### Q4: How did you calculate the lower and upper bounds of Beverly&#x27;s estimate? A4: To calculate the lower bound, we subtracted $$4\%$$ of the actual height from the actual height. To calculate the upper bound, we added $$4\%$$ of the actual height to the actual height. ### Q5: What is the formula for calculating the lower and upper bounds of an estimate? A5: The formula for calculating the lower bound is: $$\text{Lower Bound} = \text{Actual Value} - (\text{Percent Error} \times \text{Actual Value}) </span></p> <p>The formula for calculating the upper bound is:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>Upper Bound</mtext><mo>=</mo><mtext>Actual Value</mtext><mo>+</mo><mo stretchy="false">(</mo><mtext>Percent Error</mtext><mo>×</mo><mtext>Actual Value</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\text{Upper Bound} = \text{Actual Value} + (\text{Percent Error} \times \text{Actual Value}) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Upper Bound</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord text"><span class="mord">Actual Value</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord">Percent Error</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">Actual Value</span></span><span class="mclose">)</span></span></span></span></span></p> <h3>Q6: How do you determine the percent error in an estimate?</h3> <p>A6: To determine the percent error in an estimate, you need to calculate the difference between the actual value and the estimated value, and then divide that difference by the actual value. Multiply the result by 100 to get the percent error.</p> <h3>Q7: What is the importance of estimating in mathematics?</h3> <p>A7: Estimating is an important concept in mathematics because it helps us to make predictions and decisions based on incomplete or uncertain information. It also helps us to understand the relationship between different variables and to make informed decisions.</p> <h3>Q8: How do you use estimation in real-world applications?</h3> <p>A8: Estimation is used in many real-world applications, such as finance, engineering, and science. For example, in finance, estimation is used to predict stock prices and interest rates. In engineering, estimation is used to design and build structures and systems. In science, estimation is used to make predictions and understand complex phenomena.</p> <h2>Conclusion</h2> <p>In this article, we answered some frequently asked questions related to the actual height of a book and Beverly's estimated height. We also discussed the importance of estimation in mathematics and how it is used in real-world applications.</p> <h2>Frequently Asked Questions</h2> <ul> <li>What is the actual height of the book?</li> <li>What is Beverly's percent error?</li> <li>What is the range of values that represents Beverly's estimated height?</li> <li>How did you calculate the lower and upper bounds of Beverly's estimate?</li> <li>What is the formula for calculating the lower and upper bounds of an estimate?</li> <li>How do you determine the percent error in an estimate?</li> <li>What is the importance of estimating in mathematics?</li> <li>How do you use estimation in real-world applications?</li> </ul> <h2>References</h2> <ul> <li>[1] &quot;Percent Error.&quot; Math Is Fun, <a href="http://mathisfun.com/percentage/percent-error.html">mathisfun.com/percentage/percent-error.html</a>.</li> <li>[2] &quot;Estimating the Height of an Object.&quot; Math Open Reference, <a href="http://mathopenref.com/estimatingheight.html">mathopenref.com/estimatingheight.html</a>.</li> <li>[3] &quot;The Importance of Estimation in Mathematics.&quot; Mathematics, <a href="http://math.org/importance-of-estimation-in-mathematics">math.org/importance-of-estimation-in-mathematics</a>.</li> </ul> <h2>Related Articles</h2> <ul> <li>[1] &quot;The Actual Height of a Book and Beverly's Estimated Height.&quot;</li> <li>[2] &quot;How to Calculate Percent Error.&quot;</li> <li>[3] &quot;The Role of Estimation in Real-World Applications.&quot;</li> </ul>