Algebra Demystified 2nd Ed

70 algebra De mystif ieD

3. 8 · 2.5 =


4. 0.153 · 6.8 =


5. 0.0351 · 5.6 =

SOLUTIONS

1. 3.2 · 1.6 = 5.12


2. 4.11 · 2.84 = 11.6724


3. 8 · 2.5 = 20.0 = 20


4. 0.153 · 6.8 = 1.0404


5. 0.0351 · 5.6 = 0.19656

Fractions Containing Decimals

Fractions having a decimal number in their numerator and/or denominator can

be rewritten as fractions without decimal points. We multiply the numerator

and denominator by a power of 10—the same power of 10—large enough so

that the decimal point becomes unnecessary (more about this in a moment).

13

39

1310

3910

13

39

1

3

.

.

.

.

= ⋅

⋅

==

To determine what power of 10 we need, we count the number of digits

behind each decimal point.

1.28 ←Two digits behind the decimal point

4.6 ←One digit behind the decimal point

We need to multiply the numerator and denominator by 10^2 = 100 in order

to eliminate the need for decimal points.

12 8 100

46100

128

460

32

115

.

.

⋅

⋅

==

In general, if there is only one digit behind the decimal point, we multiply

the fraction by^1010 , if there are at most two digits behind the decimal point, we

multiply the fraction by^100

100

, and if there are at most three digits behind the

decimal place, we multiply the fraction by^1000

1000

. This process is called clearing
the decimal.

SOLUTIONS

1. 3.2

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