-3

Definition

-3 is a rational number that represents a quantity three units less than zero on the number line. It falls into the category of integers and is crucial in understanding the properties of numbers, especially when differentiating between positive and negative values. The significance of -3 extends to various mathematical operations, comparisons, and real-world applications, illustrating how negative numbers are used to represent debt, loss, or below-zero temperatures.

5 Must Know Facts For Your Next Test

1. -3 is an integer and also classified as a rational number since it can be represented as -3/1.
2. On a number line, -3 is located to the left of 0 and is three units away from it.
3. Negative numbers, like -3, are essential for performing operations such as subtraction and indicating values below zero.
4. -3 is often used in real-world contexts to represent deficits or losses, such as a bank account balance in the negative.
5. The absolute value of -3 is 3, which indicates its distance from zero on the number line.

Review Questions

• How does -3 compare with other rational numbers on the number line?
  • -3 is positioned to the left of 0 and all positive rational numbers on the number line, indicating that it has a lesser value compared to those numbers. When comparing -3 with other negative numbers like -2 or -4, it is greater than -4 but less than -2. This placement shows the importance of understanding the relative positions of negative numbers when performing mathematical operations.
• Explain how -3 demonstrates the properties of rational and irrational numbers.
  • -3 exemplifies the characteristics of rational numbers because it can be expressed as a fraction (-3/1). Rational numbers can be represented on the number line, showing that they have specific positions based on their value. Unlike irrational numbers, which cannot be expressed as simple fractions and have non-repeating decimal expansions, -3 has a precise location and representation, reinforcing its classification as a rational number.
• Evaluate the impact of including negative integers like -3 in mathematical operations and real-world applications.
  • Including negative integers such as -3 broadens the scope of mathematical operations by allowing for the representation of deficits or loss situations. For instance, when calculating profit and loss in finance, using -3 might signify a loss of three dollars. This inclusion helps in modeling real-life scenarios such as temperatures below freezing or financial statements showing debts. Thus, understanding negative integers enhances our ability to solve problems that reflect actual conditions.

Related terms

Rational Number: A number that can be expressed as the quotient of two integers, where the denominator is not zero.

Integer: A whole number that can be positive, negative, or zero, but does not include fractions or decimals.

Number Line: A visual representation of numbers placed in order along a straight line, where each point corresponds to a number.