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.
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.
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.
Use the multiplication pattern shown in the scientific
notation subsection.
See Example
9 and then estimate the distances.
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.
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)
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.
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.
