Problem 37 - Fundamentals of Mathematics

Question

For the following 10 problems, write the fractions using whole numbers. one three-billionths

Step-by-Step Solution

Answer

The fraction is \( \frac{1}{3,000,000,000} \).

Step 1: Understand the Fraction

The phrase 'one three-billionths' refers to the fraction where 1 is the numerator and 3 billion is the denominator.

Step 2: Recognize the Numbers

Identify the whole numbers involved: 1 is the numerator and 3 billion as the whole number denominator can be represented as 3,000,000,000.

Step 3: Write the Fraction

Combine the numbers into fraction form. The fraction is written as \( \frac{1}{3,000,000,000} \).

Key Concepts

Numerator and Denominator

Every fraction consists of two main parts: the numerator and the denominator. Understanding these components is essential for writing and interpreting fractions.
The **numerator** is the top number in a fraction. It indicates how many parts of the whole are being considered. In our example of "one three-billionths," the numerator is 1, representing a single part out of the total parts.
The **denominator** is the bottom number. It shows the total number of equal parts the whole is divided into. In this case, "three-billionths" tells us that the whole is divided into 3 billion parts, making our denominator 3,000,000,000.

• The numerator is always the number of parts you have.
• The denominator shows the total number of equal parts.
• A fraction simplifies the relationship between these two numbers.

Knowing the roles of the numerator and the denominator will help you figure out and write fractions accurately.

Whole Numbers

Fractions are often constructed from whole numbers. These are numbers without fractions or decimals; they are complete units. For the task of writing fractions, it's crucial to identify the whole numbers that will serve as the numerator and the denominator.
In the example "one three-billionths," the whole number 1 serves as the numerator, indicating the specific quantity we have. The whole number 3,000,000,000 is the denominator, representing the total division of the number.

• Whole numbers are integers with no fractional or decimal parts.
• They create the basis for establishing the fraction's structure.
• Recognizing these numbers helps simplify fractions and arithmetic tasks.

Whole numbers play a critical role in forming and understanding the basic structure of fractions.

Fraction Notation

Fraction notation is how we express parts of a whole using two numbers. It is a straightforward yet powerful way to denote the division of a whole into parts. The general form is \( \frac{a}{b} \), where \( a \) and \( b \) are whole numbers.
When writing the fraction "one three-billionths," it's represented as \( \frac{1}{3,000,000,000} \). This notation succinctly describes that we have 1 part out of a possible 3 billion.

• The forward slash or a horizontal line separates the numerator and denominator.
• This notation efficiently conveys the proportion represented by the fraction.
• It is crucial to keep fractions straightforward for better comprehension and usage.

By mastering fraction notation, you can represent any division of numbers clearly and effectively.