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Chapter 5: Problem 25

In Exercises 25-36, express each rational number as a decimal. \(\frac{3}{4}\)

Short Answer

Expert verified
\(\frac{3}{4} = 0.75\)

Step by step solution

01

Identify the Numerator and Denominator

In the fraction \(\frac{3}{4}\), the numerator is '3' and the denominator is '4'.
02

Perform the Division

To convert the fraction into a decimal, divide the numerator by the denominator. So, divide 3 by 4.
03

Write the Result

The result of the division is 0.75. This is the decimal equivalent of the fraction \(\frac{3}{4}\).

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Key Concepts

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

Decimal Conversion
The process of decimal conversion involves transforming a fraction into a decimal format. This helps in simplifying mathematical calculations. Fractions represent a part of a whole number, while decimals extend this representation into base 10 numbers, which are easier to read and calculate with.
To convert a fraction into a decimal, follow these steps:
  • Identify and write down the numerator and the denominator.
  • Perform division: divide the numerator by the denominator.
  • The result of this division will be the decimal form of the fraction.
Learning decimal conversion skills is valuable, as decimals are widely used in various fields, including finance, engineering, and science.
Numerator and Denominator
When working with fractions, it is essential to understand the terms 'numerator' and 'denominator.' A fraction consists of two parts:
  • Numerator: This is the top part of the fraction and represents how many parts of the whole are being considered.
  • Denominator: This is the bottom part of the fraction and indicates the total number of equal parts the whole is divided into.
For example, in the fractional expression \(\frac{3}{4}\), the numerator is '3' and the denominator is '4.' These components are fundamental in understanding and working with fractions, which will help in converting them to decimals.
Division
Division is a math operation that involves splitting a number into equal parts. It is crucial for converting fractions into decimals. To convert a fraction using division, follow this simple guide:
  • Take the numerator (the number on top of the fraction).
  • Divide this number by the denominator (the number on the bottom).
  • The result of this division is your decimal.
This process might involve long division if the numbers do not divide evenly. It's a good practice to understand how to handle decimal points and remainders in division. For instance, \(3 \div 4 = 0.75\). This operation turns the fraction \(\frac{3}{4}\) into its decimal equivalent.
Fraction to Decimal
Converting fractions to decimals is a straightforward yet essential mathematical process. The fraction \(\frac{3}{4}\) serves as a perfect example to demonstrate this concept.
  • Identify 3 as the numerator and 4 as the denominator.
  • Divide the numerator (3) by the denominator (4).
  • The quotient, 0.75, is the fraction expressed in decimal form.
By mastering converting fractions to decimals, you enhance your number sense, which can assist in numerous real-world applications such as measurement, probability, and algebra. It's a fundamental skill that simplifies working with numbers in diverse contexts.

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Most popular questions from this chapter

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-4, r=-2\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-\frac{1}{8}, r=-2\)

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In Exercises 129-130, suppose you save \$1 the first day of a month, \(\$ 2\) the second day, \(\$ 4\) the third day, and so on. That is, each day you save twice as much as you did the day before. What will you put aside for savings on the fifteenth day of the month?
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