1.07 Integers in the real world
Introduction
We've previously learned that integers are made up of positive and negative whole numbers, as well as the number 0. We also know that integers can be represented visually using a number line. We'll now consider some real-world applications of integers.
Represent situations with integers
Integers on their own can be used to describe real life situations. This is a convenient skill as it allows us to quickly describe or write down a situation.
The positive sign (+) and negative sign (-) in a real-world context represent the direction of the magnitude of a quantity. For example, a positive temperature represents a temperature above absolute zero, while a negative temperature represents a temperature below absolute zero.
In some situations, the positive sign indicates an increase, while the negative sign indicates a decrease.
For example, let's say that a local coffee shop is increasing the prices of all of their menu items by \$ 1. We can quickly describe this situation by writing + 1. The positive sign indicates an increase, and the 1 indicates going up by 1.
Similar to the above situation, we can also represent a decrease in price. To represent a decrease by \$3, we'll use a negative sign. Therefore, we can represent a decrease in price by \$3 by writing - 3.
Examples
Example 1
Write an integer to represent the following statement:
A loss of \$ 52.
A rise or increase in value will be represented by a positive integer.
A loss or decrease in value will be represented by a negative integer.
Practical applications of integers
When we use the number line to understand a real-world situation, we need to decide two things: where should we put 0, and what direction should be positive? In this way, the integers on the number line become signed numbers that we identify with locations in the real world. The size of the integer tells us the distance from 0, and the sign (either positive or negative) of the integer tells us the direction from 0.
Examples
Example 2
Let the location of a city be represented by the integer 0, and let a point 7\text{ km} to the east of the city be represented by the integer 7. What integer represents the point 4\text{ km} to the west of the city?
Applying a number line to real-life situations is a great way to visualize the information.