3.1 Introduction to integers

Locate positive and negative numbers on the number line

Do you live in a place that has very cold winters? Have you ever experienced a temperature below zero? If so, you are already familiar with negative numbers. A negative number    is a number that is less than $0.$ Very cold temperatures are measured in degrees below zero and can be described by negative numbers . For example, $\mathrm{-1}\text{°F}$ (read as “negative one degree Fahrenheit”) is $1\text{degree}$ below $0.$ A minus sign is shown before a number to indicate that it is negative. [link] shows $\mathrm{-20}\text{°F},$ which is $20\text{degrees}$ below $0.$

Temperatures are not the only negative numbers. A bank overdraft is another example of a negative number. If a person writes a check for more than he has in his account, his balance will be negative.

Elevations can also be represented by negative numbers . The elevation at sea level is $\text{0 feet}.$ Elevations above sea level are positive and elevations below sea level are negative. The elevation of the Dead Sea, which borders Israel and Jordan, is about $\mathrm{1,302}\text{feet}$ below sea level, so the elevation of the Dead Sea can be represented as $\mathrm{-1,302}\text{feet}.$ See [link] .

Depths below the ocean surface are also described by negative numbers. A submarine, for example, might descend to a depth of $500\text{feet}.$ Its position would then be $\mathrm{-500}\text{feet}$ as labeled in [link] .

Both positive and negative numbers can be represented on a number line    . Recall that the number line created in Add Whole Numbers started at $0$ and showed the counting numbers    increasing to the right as shown in [link] . The counting numbers $\text{(1, 2, 3, …)}$ on the number line are all positive. We could write a plus sign, $+,$ before a positive number such as $+2$ or $+3,$ but it is customary to omit the plus sign and write only the number. If there is no sign, the number is assumed to be positive.

Now we need to extend the number line to include negative numbers . We mark several units to the left of zero, keeping the intervals the same width as those on the positive side. We label the marks with negative numbers, starting with $\mathrm{-1}$ at the first mark to the left of $0,\mathrm{-2}$ at the next mark, and so on. See [link] .