/*! 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 12 Convert the given fraction to a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 12

Convert the given fraction to a terminating decimal. \(\frac{4}{8}\)

Short Answer

Expert verified
The fraction \( \frac{4}{8} \) simplifies to \( 0.5 \), a terminating decimal.

Step by step solution

01

Simplify the Fraction

To convert a fraction to a decimal, first check if it can be simplified. The given fraction is \( \frac{4}{8} \). Both the numerator and the denominator can be divided by their greatest common divisor, which is 4. Thus, \( \frac{4}{8} \) simplifies to \( \frac{1}{2} \).
02

Divide the Numerator by the Denominator

After simplifying, use division to convert the fraction to a decimal. Divide the numerator (1) by the denominator (2). Perform the division: \( 1 \div 2 = 0.5 \).
03

Verify the Decimal is Terminating

A terminating decimal has a finite number of digits after the decimal point. The result from the division is \( 0.5 \), which has one digit after the decimal point, confirming it is a terminating decimal.

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.

Simplifying Fractions
Simplifying fractions is the process of reducing a fraction to its simplest form. This means adjusting the numerator and the denominator until they no longer have any common factors other than 1. For instance, the fraction \( \frac{4}{8} \) can be simplified. Both the numbers 4 and 8 share a common factor of 4.
  • Divide the numerator (4) and the denominator (8) by their greatest common divisor (GCD), which is 4.
  • The simplified fraction is \( \frac{1}{2} \). This form is easier to work with and can make future calculations simpler.
  • Recognizing the GCD is a key skill in simplifying fractions; with practice, this becomes second nature.
By simplifying fractions, you lay the groundwork for converting fractions to decimals more effectively.
Terminating Decimals
Terminating decimals are decimals that have a set number of digits after the decimal point. They do not go on forever, unlike repeating decimals. When converting fractions like \( \frac{1}{2} \) to decimals, you often end up with a terminating decimal.
  • The decimal equivalent of \( \frac{1}{2} \) is 0.5, which is a terminating decimal because it only has one digit after the decimal point.
  • A terminating decimal is an indicator that the fraction has been divided wholly and finitely.
  • To identify if a decimal is terminating, you could look for factors of the denominator. If after simplification, the denominator consists solely of the prime factors 2 and/or 5, the decimal will terminate.
Terminating decimals are straightforward and clear, enhancing comprehension of the specific value without ambiguity.
Division Method for Fractions
The division method for converting fractions to decimals is both practical and straightforward. In this process, you divide the numerator by the denominator. Let's explore how this works using our example of \( \frac{1}{2} \).
  • Place the numerator (1) inside the division bracket and the denominator (2) outside.
  • Divide 1 by 2. Since 1 is smaller than 2, it enters into the bracket as 0, and you add a decimal point.
  • Create a zero in the tenths place, making it 10, and then divide again: 10 divided by 2 gives a quotient of 5.
  • The result is 0.5, confirming \( \frac{1}{2} \) equals 0.5 as a decimal.
Using the division method for fractions is reliable for converting both simple and complex fractions into decimals and ensures accuracy every step of the way.

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

Compute the exact square root. \(\sqrt{4.84}\)

Divide the decimals. \(\frac{-2.025}{-0.75}\)

Compute the exact square root. \(\sqrt{\frac{100}{81}}\)

Simplify the given expression. \(\frac{1.5(-8.8)-(-18.6)}{1.8}\)

Convert the given fraction to a terminating decimal. \(\frac{9}{24}\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

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.