Years ago, negative numbers often puzzled people. One mathematician called negative numbers “ghostly” - for how could there be less than nothing of something?
Nowadays, however, if the temperature should drop to -10°F, no one would ring up the Meteorological Office to complain that this negative number was ghostly or unreal.
When we multiply or divide powers of numbers, we sometimes obtain exponents of zero. We also obtain exponents of less than zero. Before we begin dealing with these negative exponents, it will be wise to review the rules of arithmetic for negative numbers.
A number written without a sign is usually read as a positive number. In this lesson on adding and subtracting signed numbers, we shall write the + sign on numbers that are positive. We shall put the sign and the number in parentheses, as in ( + 7), when there might otherwise be some confusion.
Sometimes we want to speak of the “size” of a number without reference to its positive or negative “quality”. In speaking of a number this way, we refer to what is known as its absolute value or magnitude. Thus, the absolute values of +7 and -7 are the same: 7. The absolute value of -13 is 13, the absolute value of +26 is 26. So the absolute value, or magnitude, of a number is simply the number itself regardless of sign.