160 Review Questions and Answers
Chapter 7Question 7-1
What does it mean to raise a number to the power of 2? To the power of 3? To the power of n,
where n is any positive integer?Answer 7-1
When we raise a number to the power of 2, we multiply it by itself. This is also called squar-
ing the number. When we raise a number to the power of 3, we multiply it by itself, and then
multiply the result by the original number again. This is also called cubing the number. In
general, if b is any number and we raise it to the power of n, we havebn=b×b×b× ... ×b (n times)Question 7-2
What is an order of magnitude in the decimal system?Answer 7-2
An order of magnitude is a way to express how many times larger or smaller a certain quantity
is, in terms of absolute value, compared to another quantity. In the base-10 system:- When quantities differ by one order of magnitude, then the absolute value of one
quantity is 10 times larger than the absolute value of the other. - When quantities differ by two orders of magnitude, then the absolute value of one
quantity is 10^2 , or 100, times larger than the absolute value of the other. - When quantities differ by n orders of magnitude, then the absolute value of one quan-
tity is 10n times larger than the absolute value of the other.
Question 7-3
What is the 0th (or zeroth) power of a nonzero number?Answer 7-3
When we raise any number except 0 to the power of 0, we get 1. The 0th power of 0 is not
defined. So, for example, 369^0 = 1 and (−87/16)^0 = 1, but 0^0 is undefined.Question 7-4
What’s the difference between a terminating decimal and an endless decimal? What’s the dif-
ference between an endless repeating decimal and an endless nonrepeating decimal?Answer 7-4
A terminating decimal has a finite number of digits to the right of the decimal point. After
that, they are no more nonzero digits. (If we want to add more digits, e.g., to indicate a cer-
tain level of accuracy in a physics experiment, then the digits will all be ciphers.) Here’s an
example:25-4/100= 25.04