/*! 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 36 Find decimal notation. \(\frac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 36

Find decimal notation. \(\frac{5}{12}\)

Short Answer

Expert verified
0.4167

Step by step solution

01

Understand the Problem

Determine the decimal representation of the fraction \(\frac{5}{12}\). This involves division of the numerator by the denominator.
02

Set Up the Division

Set up the division where 5 is divided by 12. Here, 5 is the dividend (inside the division bracket) and 12 is the divisor (outside the division bracket).
03

Perform the Division

Divide 5 by 12. Since 5 is less than 12, we put a decimal point and add zero. This makes it 50. Dividing 50 by 12 gives approximately 4, with a remainder of 2. Bring down another zero making it 20, and divide by 12 giving about 1. Continue this process.
04

Continue Until Sufficient Precision

The process generates a repeating decimal. \(\frac{5}{12} \) = 0.41666... (rounded, it's approximately 0.4167 if rounded to four decimal places).

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.

fraction to decimal conversion
Converting a fraction to its decimal form is essential in math. This process involves dividing the numerator (top number) by the denominator (bottom number). For instance, with the fraction \( \frac{5}{12} \), you're dividing 5 by 12. This conversion is useful for understanding and comparing sizes of different fractions easily. Whether you're adding, subtracting, or comparing fractions, moving to a decimal can simplify the process.
Remember, the goal of this conversion is to find a way to write the fraction as a number with a decimal point.
division process
The division process is crucial for converting fractions to decimals. Let's dive into the steps:
  • Step 1: Identify the numerator and denominator. Here, 5 is the numerator, and 12 is the denominator.
  • Step 2: Set up your division format. Place the numerator (5) inside the division bracket and the denominator (12) outside.
  • Step 3: Begin dividing. Since 5 is smaller than 12, you need to add a decimal point and a zero, making it 50.
  • Step 4: Divide 50 by 12 to get 4, put 4 in the quotient, and bring down the remainder.
  • Step 5: Continue with more zeros and dividing until you reach the desired precision. For example, after dividing several times, you notice the decimal starts repeating.
This process might seem long, but it's straightforward with practice. Keep dividing and bringing down zeros until you've achieved enough decimal places.
repeating decimal
A repeating decimal is a decimal number that has one or more repeating digits after the decimal point. When converting \( \frac{5}{12} \) to a decimal, you'll notice the sequence 6 keeps repeating: 0.41666...
This is shown as 0.41\( \overline{6} \). If a decimal repeats, it means that division will continue producing the same result.
Thus, recognizing a repeating decimal helps simplify and understand exact fraction to decimal conversions. Not all decimals terminate; some keep repeating or continue infinitely, making it important to spot and denote repeating patterns. In math, it's common to see this represented with a bar over the repeating digits.

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

Add. $$ \begin{array}{r} 4203.28 \\ +\quad 3.39 \\ \hline \end{array} $$

Estimate. Indicate which of the choices is an appropriate estimate. \(234.12321-200.3223\) a) 600 b) 60 c) 300 d) 30

Simplify. $$ 3 \cdot 60-(12+3) $$

Add. $$ 2.3+0.729+23 $$

Claire bought a copy of the book Make Way for Ducklings for her daughter for \(\$ 16.95\) plus \(\$ 0.85\) sales tax. She paid for it with a \(\$ 20\) bill. How much change did she receive?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

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.