This is a problem, because losing one zero is a much more significant change than going from “27…” to “28….” If we use scientific notation, the loss of a zero is more apparent because it makes the expression change from 2.7 × 109 to 2.7 × 108. If we write this as 2,700,000,000 W (or worse, 2700000000 W, without the commas), we will be focusing on the “27.” We will readily notice a change from “27” to “28,” but we could easily fail to notice the loss of a zero. In some cases, the important information is the power of ten.įor example, if we’re discussing the electricity-generating capacity of a nuclear power plant, we might see the value 2.7 × 109 W. Scientific notation also helps us to focus on the more important information. It is widely used in science and engineering, and (as you can see in the third example), it can save a lot of time and space when we’re working with numbers that are extremely small or extremely large. This method of writing (and saying) numbers is called scientific notation. We can represent any value by combining these powers of ten with other numbers. The following small numbers are frequently expressed as powers of ten or as the corresponding prefixes: The concept is the same, but the superscript number has a negative sign that causes the overall expression to become the denominator of a fraction in which the numerator is 1. Powers of ten can also be used for very small numbers. The following large numbers are frequently expressed as powers of ten (or as prefixes, discussed later in this page, that correspond to a power of ten). A power of ten is expressed in writing as “10” along with a superscript number indicating how many tens should be multiplied together. Nowadays people use the decimal system for almost everything we also interact frequently, though usually indirectly, with the binary system, which is the basis of the computational activity performed by digital circuits.Īs the name implies, the decimal system is built around the number ten, and engineers commonly use powers of ten when working with large numbers. Currently, the dominant numeral systems are the decimal (or base-ten) system and the binary (or base-two) system. A numeral system is a method of using certain digits to represent numerical quantities.
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