The quotient of two algebraic expressions is called a fraction. The exponent only applies to the x, not the 3. If a number is written in scientific form and we want to rewrite it in standard form, we simply reverse the above procedure. The exponent is positive if the decimal point has been moved to the left and it is negative if the decimal point has been moved to the right. Multiply the result by a power of ten with an exponent equal to the number of places the decimal point was moved.
Move the decimal point so that there is one nonzero digit to the left of the decimal point. In this case, 5.7 x 10 3 is the scientific form for 0.0057. Now, let us consider some factored forms of 0.0057 in which one of the factors is a power of 10. A number expressed as the product of a number between 1 and 10 (including 1) and a power of 10 is said to be in scientific form or scientific notation. We can also rewrite small numbers by using powers with negative exponents that have been introduced in this section.įirst, let us consider some factored forms of 38,400 in which one of the factors is a power of 10.Īlthough any one of such factored forms may be more useful than the original form of the number, a special name is given to the last form. Large numbers can be rewritten in a more compact and useful form by using powers with positive exponents. Thus, for any a not equal to 0, we can view a -3 as equivalent to. Using the two quotient laws for powers, we have Note that for any a not equal to zero, the left-hand member equals 1 and the right-hand member equals a 0. Using the property of quotients of powers, we have First, let us consider the quotient a 4/a 4. 
We will now give meaning to powers in which the exponent is 0 or a negative integer. Recall that we have defined a power a n (where n is a natural number) as follows: In this section, we will introduce another symbol for a fraction of the form and then we will use this symbol to write certain numbers in simpler form. INTEGER EXPONENTS AND SCIENTIFIC NOTATION
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