Problem 24 - Introductory and Intermediate Algebra for College Students 4th

Question

Express each rational number as a decimal. $$\frac{3}{20}$$

Step-by-Step Solution

Answer

The decimal representation of \(\frac{3}{20}\) is 0.15

Step 1: Identify the numerator and the denominator

In this case, the given rational number is \(\frac{3}{20}\). Here, 3 is the numerator, and 20 is the denominator.

Step 2: Perform the division operation

Perform the division operation where the numerator is divided by the denominator. That is, divide 3 by 20.

Step 3: Write down the decimal result

After performing the division, the result obtained is the required decimal number.

Key Concepts

Decimals

Decimals are a way to represent numbers that are not whole. They provide a way to express parts of a whole number in a format that is easy to understand and work with. Decimals are based on the powers of ten, making them closely related to our everyday counting system.
In the given problem, we convert the fraction \(\frac{3}{20}\) into a decimal. This process involves dividing the numerator by the denominator, resulting in a decimal value. The decimal point, which separates the whole number part from the fractional part, is crucial.

• The number to the left of the decimal point represents the whole number.
• The numbers to the right represent parts of a whole, gradually becoming smaller with place value.

Understanding how to work with decimals is important because they are used widely in mathematics, finance, and many real-world applications.

Numerator and Denominator

When dealing with fractions, such as \(\frac{3}{20}\), it's important to understand the terms "numerator" and "denominator."
The numerator is the top number in a fraction. It represents how many parts of the whole are being considered. In this case, the numerator is 3, which indicates we have 3 parts of something that is divided into smaller sections.
The denominator is the bottom number, telling us into how many equal parts the whole is divided. Here, the denominator is 20, signifying that the whole is divided into 20 equal parts.

• The numerator helps in determining the size or quantity of what we are measuring.
• The denominator provides a sense of the scale of these measurements, increasing the clarity of what the fraction represents.

By understanding these concepts, you can more easily transition from fractions to decimals, enabling a smoother conversion process and comprehension.

Division Operation

The division operation is central to converting fractions into decimals. In our example, we need to divide 3 (the numerator) by 20 (the denominator). This operation tells us how many times the denominator can fit into the numerator, or in decimal terms, how much each part represented by the numerator contributes to the whole.
To carry out the division operation and convert \(\frac{3}{20}\) to a decimal, follow these steps:

• Place the numerator (3) inside the division bracket and the denominator (20) outside.
• Perform the division. If 20 does not go into 3 whole times, place a zero before the decimal point in the quotient.
• Add a decimal point and proceed with normal division, bringing down numbers for a more accurate result.

Utilizing the division operation effectively allows us to switch between different numerical representations easily, widening our understanding of numbers in various forms. It is a fundamental skill in math, useful in a multitude of scenarios.