Problems 1-6
Even if your instructor does not assign these problems, you will do much better in understanding the material in the book if you spend about 20 minutes answering these questions. Remember, the problems labeled “In Your Own Words,” do not have right or wrong answers. What is important is that you think about these questions. For example, take a look at Problem 3 : DO YOU PLAN ON USING A CALCULATOR IN THIS COURSE? If so, then you should know the answer to this question for your own calculator.
Problems 7-10
See Example 2; scientific notation is to write the number as a number between 1 and 10 times a power of ten, and floating-point notations refers to calculator notation. The form given in the book is called fixed point notation. Rewrite each number with a decimal point following the first digit, and then multiply by an appropriate power of ten.
For example, Problem 7a: 3,200 = 3.200 * 10^3.
Don’t forget floating-point notation, as well: 3.2 03
Hint for Problem 10a; look at Table 1.1.
Problems 11-14
See Examples 1 (for part a), and Example 7 (for parts b and c). The form given in part a is called exponential notation. Notice that negative exponents are fractions, not necessarily negative numbers. The form given in part b is called scientific notation, and in part c is called floating-point notation.
Problems 15-18
See Example 3 for the set-up and then Example 1 for the conversions. Don’t forget to do this for all the numbers in each question. All but one of these problems has two numbers to convert to scientific notation.
Problems 19-22
Use the multiplication pattern shown in the scientific notation subsection.
Problems 23-24
See Example 9 and then estimate the distances.
Problems 25-30
Estimation is a skill that is difficult to learn, and even more difficult to teach. You must build your estimation skills by practice. You need to work at estimating every time you work a calculation problem. You cannot learn good estimation skills if you do not practice them on a daily basis. After estimating, carry out the arithmetic calculations (it is ok to use a calculator) and then compare your estimates and calculated answers.
Problems 31-36
See Examples 4-7; use a calculator or use the laws of exponents. Look at Problem 32b , for example: Here is how you would input it into your calculator. If the numerator or denominator of a fraction includes more than a single number, you must remember to insert parentheses:
([(6 * 10^(-3)][7 * 10^8])/(3 * 10^7).
If you do this without a calculator, group together the number parts and the base 10 parts:
(6 * 7)/3 * [10^(-3)*10^8]/10^7
= 42/3 * 10^(-3 + 8 – 7)
= 14 * 10^(-2)
Problems 37-40
Estimation is a skill that is difficult to learn, and even more difficult to teach. For these problems count the number of objects in one quarter of the photograph and then use this result as an estimate for the total number in the picture.
Problems 41-48
See Examples 8 and 9, and also use Examples 10 and 11 to help you with your problem-solving skills. Use scientific notation whenever possible.
Problems 41-44 are designed to give you an intuitive concept of large numbers.
For Problem 44, grab a stack of pennies and count the number in one inch.
For Problem 45, work in scientific notation.
Note: Homework Hints are given only for the Level 1 and Level 2 problems.
However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section). As a last resort, you can call the author at (707) 829-0606.
On the other hand, the problems designated “Problem Solving” generally require techniques that do not have textbook examples.
There are many sources for homework help on the internet.
Algebra.help
Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.
http://www.algebrahelp.com/
Quick Math
This site provides online graphing calculators. This is especially useful if you do not have your own calculator.
http://www.quickmath.com/
The Math Forum @ Drexel
This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.
http://mathforum.org/