Problems Manual for use with Grob’s Basic Electronics
In the fi eld of electronics, the magnitudes of the various units are often extremely small or extremely large. For example, in electronics it is not at all uncommon to work with extremely small decimal fractions such as 0.000000000047 or extremely large numbers such as 100,000,000. To enable us to work conveniently with both very small and very large numbers, powers of 10 notation is used. Powers of ten notation allows us to express any number, no matter how large or how small, as a decimal number multiplied by a power of 10. A power of 10 is an exponent written above and to the right of 10, which is called the base. The power or exponent indicates how many times the base is to be multiplied by itself. For example, 102 means 10 3 10 and 104 means 10 3 10 3 10 3 10. In electronics, the base 10 is common because multiples of 10 are used in the metric system of units. As you will see, powers of 10 allow us to keep track of the decimal point when working with extremely small and extremely large numbers.
Positive powers of 10 are used to indicate numbers greater than 1, and negative powers of 10 are used to indicate numbers less than 1. Table I-1 shows the powers of 10 ranging from 10212 to 109. As you will discover in your study of electronics, seldom will you encounter powers of 10 which fall outside this range. From Table I-1 notice that 100 5 1 and 101 5 10. In the case of 100 5 1, it is important to realize that any number raised to the zero power equals 1. In the case of 101 5 10, it is important to realize that any number written without a power is assumed to have a power of 1.
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