/*! 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 15 Read each decimal fraction by wr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 15

Read each decimal fraction by writing it. 0.78

Short Answer

Expert verified
0.78 is equivalent to \(\frac{39}{50}\) as a fraction.

Step by step solution

01

Understand the Decimal

The decimal 0.78 is a number between 0 and 1. The number after the decimal point represents parts of a whole.
02

Identify the Place Values

Identify the position of each digit after the decimal point: the first digit '7' is in the tenths place, and the second digit '8' is in the hundredths place.
03

Write the Decimal as a Fraction

Convert the decimal to a fraction by using the place value. Since the last digit, 8, is in the hundredths place, 0.78 is equivalent to the fraction \(\frac{78}{100}\).
04

Simplify the Fraction

Simplify \(\frac{78}{100}\) by finding the greatest common divisor (GCD) of 78 and 100, which is 2. Divide numerator and denominator by 2 to get \(\frac{39}{50}\).

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.

Understanding Place Value
Place value is a fundamental concept in understanding numbers, especially decimals. When you look at a decimal like 0.78, you'll notice the decimal point separates the whole number part from the fractional part. Each digit after the decimal point has a specific position that determines its value.

Let's break down 0.78 to see how place value works:
  • The '7' is the first digit after the decimal point, so it is in the \'tenths\' place. This means the 7 represents \(7 \times \frac{1}{10}\) or 0.7.
  • The '8' is the second digit after the decimal point, placing it in the \'hundredths\' place. This means it represents \(8 \times \frac{1}{100}\) or 0.08.
Using place value, we see that 0.78 can be understood as the sum of 0.7 and 0.08.
Decimal to Fraction Conversion
Converting decimals to fractions is an essential skill. It enables an easier visualization of parts of a whole, which can simplify many math problems.

To convert the decimal 0.78 to a fraction,
  • Write the decimal as a fraction where the digits after the decimal are the numerator, and the place value is the denominator. Since '78' comes after the decimal, and the last place value mentioned is hundredths, you write 0.78 as \( \frac{78}{100} \).
This represents the 78 parts out of 100, aligning directly with the hundredths place value for this decimal.
Simplifying Fractions
Simplifying fractions makes them easier to work with by reducing them to their simplest form. To simplify the fraction \( \frac{78}{100} \), follow these steps:

  • Find the greatest common divisor (GCD) of the numerator and the denominator. For 78 and 100, the GCD is 2.
  • Divide both the numerator and the denominator by the GCD. So, \( \frac{78}{100} \) becomes \( \frac{78 \div 2}{100 \div 2} = \frac{39}{50} \).
  • This means that \( \frac{39}{50} \) is the simplest form of \( \frac{78}{100} \), where there are no common factors other than 1 between 39 and 50.
Always check that both terms of the fraction don't have any more common factors other than 1 to ensure you've simplified it completely.

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

Perform the following operations. \(\frac{\frac{0.32}{12}}{\frac{12}{0.35}}\)

Write each decimal using digits. Nine and twelve-hundredths.

Read each decimal by writing it in words. 8.105

Convert each fraction to a decimal. $$ \frac{43}{100} $$

Convert each decimal to a proper fraction or a mixed number. 0.05
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

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.