if the decimal point was shifted n places to the left . Module III Chapter 4 Notes (Module III, page 43)
Negative Exponents and Decimal Numbers
The properties of exponents are found on page 43 of Module III .
A negative exponent gives us a short hand for writing the reciprocal of a number . For instance , the reciprocal of 5 is 1/5 but in exponential form we say the reciprocal of 5 is 5-1 .
Example:What is the reciprocal of 3-1 ? Is it 1/3 or 3 ?
The properties of exponents show us that 3-1 = 1/3 and the reciprocal of 1/3 is 3 . Thus the reciprocal of 3-1 is 3.
The last section of Module III talks about scientific notation . It is important to see the difference between scientific notation and the expanded notation discussed in Module I (page 21) and Module III ch 2 .
Procedure for converting a number to scientific notation:
1. Move the decimal point in the number so that there is one non-zero digit before the decimal point.
2. Multiply by if the decimal point was shifted n places to the left .
Multiply by
if the decimal point was shifted n places to the right.
Example:
8,252,000 = 8.252 x 106 in scientific notation .
.0001245 = 1.245 x 10-4 in scientific notation .
What are these same numbers in expanded notation ?
What determines whether the 10 will have a negative or positive exponent ?
Note: Although it is true that 8,252,000 = 825.2 x 104 , this is not scientific notation . Why ?