Positive & Negative Numbers in the Real World

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  • 0:03 Positive and Negative Numbers
  • 1:22 Numbers in the Real World
  • 3:05 Applications
  • 4:47 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

Positive and negative numbers show up everywhere in the world around us. This lesson will go over the definition of these two types of numbers and discuss a few examples of how they are used in everyday life.

Positive and Negative Numbers

Isn't it interesting how much the temperature can vary across the world on any given day? For example, it could be 82 degrees above zero in Hawaii and at the same time be 5 degrees below zero in Alaska! Considering how much the temperature can vary depending on where you are in the world, it's good that we have different types of numbers available to represent them. For example, the temperature of 82 degrees above zero is a positive number, and we write it as 82, whereas the temperature of 5 degrees below zero is a negative number, and we write it as -5.

Technically speaking, we have the following:

  • A positive number is a number that is greater than zero. It falls above zero on a vertical number line or to the right of zero on a horizontal number line.

  • A negative number is a number that's less than zero. It falls below zero on a vertical number line or to the left of zero on a horizontal number line.

Notice that if we think of our thermometers as vertical number lines, 82 falls above zero and -5 falls below zero, as we would expect from the definitions of positive and negative numbers.

Well, that's pretty neat, and guess what? It doesn't end there! Let's explore some other instances of positive and negative numbers in the real world!

Numbers in the Real World

Another interesting area in which positive and negative numbers show up is elevation. The elevation of a location is its distance above or below sea level.

If we consider the fact that sea level has an elevation of zero, you can probably guess which type of number corresponds to above sea level and which type of number corresponds to below sea level. Since positive numbers lie above zero, they must correspond to elevations that are above sea level, and since negative numbers lie below zero, they must correspond to elevations that are below sea level.

Consider the city of New Orleans, Louisiana. New Orleans often experiences flooding, because some areas of New Orleans actually lie below sea level! For instance, one of the lowest elevations in New Orleans is at 6.5 feet below sea level, so we say the elevation is -6.5 feet, a negative number. On the other hand, one of the highest elevations in New Orleans is at 23 feet above sea level, so we say the elevation is 23 feet, a positive number.

Here's another example: You're likely reading this on a computer or a smartphone. Your device takes electricity to work, and electricity has to do with the charges of three particles: electrons, neutrons, and protons. Each of these particles contain charges that allow electricity to work as it does. Electrons contain a negative charge, and are therefore associated with negative numbers. Protons contain a positive charge, and are therefore associated with positive numbers. Neutrons are neutral, meaning they don't have a positive or a negative charge, so you can think of these as having a charge of zero.

Wow! Positive and negative numbers seem to show up everywhere around us. Let's take a look at an application of these numbers.

Applications

Suppose Sarah used her bankcard while she ran the following errands today:

  1. Went grocery shopping and spent $41.00
  2. Went to the bank and deposited $320.00
  3. Met up with a friend for lunch and spent $17.00
  4. Sent in a payment for her electricity bill of $84
  5. Received an electronic refund on her bank card of $35

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