/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 The White House covers an area o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 24

The White House covers an area of 0.028 square mile. What fraction of a square mile is this?

Short Answer

Expert verified
The area of the White House is \(\frac{7}{250}\) of a square mile.

Step by step solution

01

Understanding the Problem

We are given that the White House covers an area of 0.028 square mile. We need to express this area as a fraction of a square mile.
02

Representation as a Fraction

Any decimal can be represented as a fraction. Here, 0.028 can be represented as \(\frac{28}{1000}\) because 0.028 means 28 thousandths.
03

Simplifying the Fraction

Simplify the fraction \(\frac{28}{1000}\) by finding the greatest common factor of 28 and 1000, which is 4. Divide both the numerator and the denominator by 4 to simplify: \(\frac{28 \div 4}{1000 \div 4} = \frac{7}{250}\).
04

Final Fraction

The simplified fraction that represents the area of the White House relative to a square mile is \(\frac{7}{250}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Decimal to Fraction Conversion
Converting a decimal to a fraction might seem challenging at first, but it's a straightforward process once you understand the steps involved. A decimal number like 0.028 can be transformed into a fraction by recognizing its place value.

Each decimal digit represents a specific place value:
  • The first digit after the decimal point is the tenths place.
  • The second is the hundredths place.
  • The third is the thousandths place.

In our example, 0.028 has three digits after the decimal, placing the number 28 in the thousandths position. This means that 0.028 can be expressed as a fraction with 28 as the numerator and 1000 as the denominator, or \(\frac{28}{1000}\).

Understanding how each decimal converts into a fraction lays a firm foundation for further simplification.
Simplifying Fractions
After converting a decimal to a fraction, the next step is to simplify it. Simplifying a fraction means reducing it to its simplest form. Simplifying fractions makes them easier to read and work with in calculations or comparisons.

To simplify \(\frac{28}{1000}\), we need to divide both the numerator (28) and the denominator (1000) by their Greatest Common Factor (GCF). This process is known as reducing.

The GCF is the largest integer that divides both numbers without leaving a remainder. By simplifying, we ensure that the fraction represents the same quantity but with smaller and more manageable numbers.
Greatest Common Factor
The Greatest Common Factor (GCF) is crucial when simplifying fractions. It helps find the highest factor that two numbers share, allowing for the reduction of the fraction to its simplest form.

To determine the GCF of 28 and 1000, factor each number:
  • 28 can be factored as 1, 2, 4, 7, 14, 28.
  • 1000 can be factored as 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
The largest number that appears in both lists is 4, which means the GCF is 4. By dividing both 28 and 1000 by 4, the fraction \(\frac{28}{1000}\) simplifies to \(\frac{7}{250}\).

Learning to find the GCF is an essential skill in simplifying fractions and improving number sense.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In an online survey, about \(\frac{1}{4}\) of teenagers go to sleep between 9 and 10 P.M., while \(\frac{13}{50}\) of teenagers go to sleep at 12 A.M. or later. Which group is larger?

Jada has 156 coins in her collection. This is 12 more than 8 times the number of nickels in the collection. How many nickels does Jada have in her collection?

Find each sum or difference. Write in simplest form. $$\frac{3}{5}+\frac{1}{3}$$

Solve each equation. Check your solution. $$-6=\frac{3}{5} a$$

Use exponents to write the prime factorization of each number or monomial. 12\(n\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.