Problem 32 - Elementary and Intermediate Algebra

Question

Write decimal notation for each number. $$ \frac{1}{4} $$

Step-by-Step Solution

Answer

0.25

Step 1 - Understand the Fraction

Recognize that the fraction \(\frac{1}{4}\) consists of the numerator (1) and the denominator (4).

Step 2 - Perform the Division

Divide the numerator by the denominator: \(\frac{1}{4} \). This is the same as 1 divided by 4.

Step 3 - Calculate the Decimal

Perform the division: 1 divided by 4 equals 0.25.

Step 4 - Write the Final Answer

The decimal notation of \(\frac{1}{4}\) is 0.25.

Key Concepts

Understanding Fractions

A fraction represents a part of a whole. It is written in the form \(\frac{a}{b}\), where \(a\) is the numerator and \(b\) is the denominator. The numerator indicates how many parts we have, while the denominator shows how many parts the whole is divided into. For example, in the fraction \( \frac{1}{4} \), 1 is the numerator, and 4 is the denominator. This means we have 1 part out of a total of 4 equal parts.

Identifying the Numerator

The numerator is the top number in a fraction. It tells us the number of equal parts we have. In the fraction \( \frac{1}{4} \), the numerator is 1. This means we are considering 1 part out of the 4 parts that make up the whole. By understanding the numerator, we get an idea of how much of the whole we are working with.

Understanding the Denominator

The denominator is the bottom number in a fraction. It shows into how many equal parts the whole is divided. In the fraction \( \frac{1}{4} \), the denominator is 4, indicating that the whole is divided into 4 equal parts. A larger denominator means the parts are smaller, and a smaller denominator means the parts are larger. The denominator helps us understand the size of each part in the fraction.

Division in Algebra

In algebra, fractions can be understood using division. The fraction \( \frac{1}{4} \) can be interpreted as 1 divided by 4. Performing this division helps convert the fraction into a decimal. To convert \( \frac{1}{4} \) to a decimal, we divide 1 by 4, which equals 0.25. Thus, \( \frac{1}{4} \) in decimal notation is 0.25. Understanding that fractions represent division allows us to easily switch between fractions and decimals.