Final answer:
In arithmetic operations involving powers of 10, shortcuts can be used: move the decimal point right when multiplying and left when dividing by powers of 10. For subtracting numbers in exponential form, normalize them to the same power of 10 before subtracting.
Step-by-step explanation:
When working with powers of 10, certain shortcuts can be used to simplify calculations, especially in multiplication and division. Multiplying by powers of 10 involves moving the decimal point to the right for each zero in the power of 10. For example, multiplying 3 by 102 (or 100) shifts the decimal two places to the right, resulting in 300.
Conversely, dividing by powers of 10 requires moving the decimal to the left by the number of zeros in the power of ten. So, for instance, dividing 300 by 102 (or 100) moves the decimal two places to the left, which gives us 3.
Moreover, when dealing with the subtraction of exponentials, one approach is to convert all numbers to the same power of 10, subtract the digit terms, and then, if needed, adjust the result so that it falls between 1 and 10, by changing the power of the exponential term correspondingly.