Algebra Demystified 2nd Ed

Chapter 3 DeCiMalS 67

SOLUTIONS

1. 1.71 = 1 171
   100
   10071 =


2. 34.598 = 34 34 598
   1000
   1000598 = ,


3. 0.6 =^6
   10


4. 0.289421 = 289 421
   1 000 000

,

,,

There are two types of decimal numbers—terminating and nonterminating.

The numbers in the above problems are terminating decimal numbers. A

nonterminating decimal number has infinitely many nonzero digits following

the decimal point. For example, 0.333333333... is a nonterminating decimal

number. Some nonterminating decimal numbers represent fractions, such as

0.333333333... =^13. But some nonterminating decimals, such as π =

3.1415926654... and 2 = 1.414213562..., do not represent fractions. We

will be concerned mostly with terminating decimal numbers in this book.

We can add as many zeros at the end of a terminating decimal number as

we want because the extra zeros can be divided out.

07 7

10

070 70

100

710

10 10

7

10

0 700^700

1000

7

=

==⋅

⋅

=

==⋅^1100

10 100

7

⋅ 10

=

Adding and Subtracting Decimal Numbers

In order to add or subtract decimal numbers, each number needs to have the same

number of digits behind the decimal point. Writing the problem vertically helps

us avoid the common problem of adding the numbers incorrectly. For instance,

1.2 + 3.41 is not 4.43. The “2” needs to be added to the “4,” not to the “1.”

1.20 (Add as many zeros at the end as needed.)

• 4.43
  5.63

SOLUTIONS

1. 1.71

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