/*! 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 8 Convert the given fraction to a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 8

Convert the given fraction to a terminating decimal. \(\frac{7}{175}\)

Short Answer

Expert verified
The terminating decimal of \(\frac{7}{175}\) is 0.04.

Step by step solution

01

Simplify the Fraction

Before converting the fraction to a decimal, let's simplify it. We do this by finding the greatest common divisor (GCD) of the numerator 7 and the denominator 175. The GCD is 7. So, we divide both the numerator and the denominator by their GCD:\[ \frac{7}{175} = \frac{7 \div 7}{175 \div 7} = \frac{1}{25} \]
02

Convert to a Decimal

Now that the fraction is simplified to \(\frac{1}{25}\), convert it to a decimal. To do this, divide the numerator by the denominator:\( 1 \div 25 = 0.04 \) Hence, the decimal representation is 0.04.

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
Fractions are often not in their simplest form. Simplifying a fraction means reducing it so that the numerator and the denominator have no common factors other than 1.

To simplify a fraction:
  • Identify the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCD.
This results in a fraction that is equivalent to the original, but in a simpler state.

For example, in the fraction \(\frac{7}{175}\), we find that the GCD is 7. Simplifying it involves dividing both 7 (numerator) and 175 (denominator) by 7, resulting in \(\frac{1}{25}\). This process makes calculations, like converting to decimals, much easier.
Greatest Common Divisor
The greatest common divisor (GCD) is the highest number that divides exactly into two or more numbers.

To find the GCD:
  • List the factors of each number.
  • Identify the largest factor that both numbers share.
Using the GCD helps in simplifying fractions, as it shows the largest fraction by which both the numerator and denominator can be divided evenly.

For instance, with the numbers 7 and 175, their GCD is 7 because 7 is the largest number that exactly divides both numbers. Thus, \(\frac{7}{175}\) simplifies to \(\frac{1}{25}\). Calculating the GCD can save time and ensures the fraction is simplified correctly.
Terminating Decimals
Decimals can be terminating or non-terminating. A terminating decimal ends after a finite number of digits.

When a fraction has a denominator that is a power of ten, converting it to a decimal will result in a terminating decimal.
To ensure a fraction converts to a terminating decimal:
  • Simplify the fraction first, as this may reduce the denominator to a form compatible with powers of ten.
  • Perform division of the numerator by the simplified denominator.
For example, the simplified form of \(\frac{7}{175}\) is \(\frac{1}{25}\). Dividing 1 by 25 gives us the terminating decimal 0.04.

Understanding that simplification and division lead to a neat ending decimal makes the conversion process straightforward.

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

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

Divide the decimals. \(\frac{0.8649}{0.93}\)

Compute the quotient \(17 / 69\), and round your answer to the nearest tenth.

In Exercises 1-28, multiply the decimals. (6.7)(0.03)

Divide the decimals. \(\frac{6.278}{8.6}\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.