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MATHEMATICS
Decimal Placement in a Product or Quotient
Multiplying and dividing decimal numbers is similar to multiplying and dividing nondecimal numbers. The main
difference is that after the multiplication or division occurs in computations involving decimals, the correct placement
of the decimal needs to be determined.
The process for multiplying decimals is as follows:
Step 1. Set up the problem as if the numbers are whole numbers, without paying specific attention to the
decimal points.
Step 2. Multiply the numbers without paying specific attention to the decimal points.
Step 3. Once the multiplication is complete, count the total number of decimal places in the factors.
Step 4. Starting from the far right end of the product, count back (to the left) the number of decimal places
you counted in step 3.
Step 5. Put the decimal point in this spot. Finished!
Examples 2.10 and 2.11 apply these steps.
Example 2.10:
Multiply 5.62 and 0.3.
__________________________________________________________________________________________
Step 1. 562
×3
Step 2. 562
×3
1686
Step 3. In this problem, we had 5.62 with 2 decimal places and 0.3 with just one decimal place.
This is a total of 3 decimal places.
Step 4. Count back 3 decimal places from the end of 1686.
Step 5. The decimal belongs between the 1 and the 6. The final answer is 1.686.
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59
MATHEMATICS
Example:
Simplify the expression: 11.4 cm  7 cm  3.06 cm
Example:
Simplify the expression: 11.4 cm  7 cm  3.06 cm
Example 2.11: ____________________________________________________________
Simplify the expression: 11.4 cm × 7 cm × 3.06 cm.
____________________________________________________________
__________________________________________________________________________________________
Step
1.1.
Step
Step1.
114
114


 306
Simplify the expression: 11.4 cm  7 cm
 3.06 cm
 306
____________________________________________________________
Step 2.
Step
2.
Step 2. 114
114
 7
Step 1.
114 
798
7987
798

798
798
×
306

306
______

306
4788
4788
 306
4788
00000
00000
00000
239400
Step 2.
+________
239400
239400
244188
114
244188
244188
 7
Step
3. In this problem,
we had 11.4 with 1 decimal place and 3.06 with 2
798 3.
798
In this
problem,
we had
with
1decimal
decimal
place and
3.06
2 with 2 decimal places. This is a
Step
Step 3.decimal
In this
problem,
wea 11.4
had
1 decimal
place
andwith
3.06
places.
This
is
total11.4
of 3 with
places.


306
This is aplaces.
total of 3 decimal places.
decimal
totalplaces.
of 3 decimal
4788
Step 4. Starting
from the far right end of the product, count back (to the
00000
Step
4.
Starting
from
the3offar
right end
of the
count
back
Step 4.left)
Count
back
decimal
places
from
the end
244188.
the
number
decimal
places
youproduct,
counted
inofstep
3. (to the
239400
left) the number of decimal places you counted in step 3.
244188
Step 5.Count
The
decimal
belongs
between
theend
4 and
the 1. The final answer is 244.188 cm.
back
3 decimal
places
from the
of 244188.
Count back 3 decimal places from the end of 244188.
Step
3. dividing
In this problem,
we had is
11.4
1 decimal place and 3.06 with 2
The process
for
aswith
follows:
Step 5. decimals
The decimal
belongs
between
the
4 and the 1. The final answer is
decimal
is a belongs
total
of 3between
decimalthe
places.
Step places.
5. 244.188
TheThis
decimal
4 and the 1. The final answer is
cm.
a
__
cm.
244.188
Step 1. Set up the problem
to be
an equivalent problem in which the divisor (b in b ) is a whole number by
Step 4. Starting from the far right end of the product, count
a back (to the
__
) the
decimal
point
in the
dividend
(a ininbstep
The processmoving
for dividing
decimals
is
as follows:
left)the
thedecimals
numberis
of
places
you counted
3. same number of places that the decimal point
The process for dividing
asdecimal
follows:
Example:
is moved in the divisor.
Step 1. Set up the
problem
todecimal
be an equivalent
problem
inofwhich
the divisor is a whole
Count
back 3to
places from
the end
244188.
Step2.
1. Set
up the
problem
be an equivalent
problem
which
thepoint
divisor
a whole
Step
When
performing
division,
theindecimal
inisthe
number
by
moving thelong
decimal
point inplace
the dividend
the same
number
of quotient
places thatdirectly above the decimal point
number
moving the decimal point in the dividend the same number of places that
in decimal
the by
dividend.
the
point
is
moved
in
the
divisor.
Step
5.
The
decimal
belongs
between
the
4
and
the
1.
The
final
answer
is
the decimal point is moved in the divisor.
244.188 cm.
Step 3. For
Divide
the equation
as ifwere
it were
number.
example,
if the problem
0.48a ÷whole
1.2, then
rewrite the problem as 4.8 ÷ 12 by
For example, if the problem were 0.48 ÷ 1.2, then rewrite the problem as 4.8 ÷ 12 by
moving
the is
decimal
point to the right in both the dividend and divisor. Alternatively,
The process for dividing
decimals
as
follows:
moving
the decimal
point to the right in both the dividend and divisor. Alternatively,
Example 2.12
applies
steps.
rewrite
thethese
problems
as:
rewrite the problems as:
Step 1. Set up the problem to be an equivalent problem in which the divisor is a whole

12 4.8
1.2 0.48
number by moving the decimal point in the dividend
the
same
of places that
1.2 00.48
.48
12 number
4.8
Example
2.12:
Simplify
the expression:
÷ 1.2.
the decimal
point
is moved
in the divisor.
__________________________________________________________________________________________
For example, if the problem were 0.48 ÷ 1.2, then rewrite the problem as 4.8 ÷ 12 by
1. right
Rewrite
thethe
problem
as and
4.8 divisor.
÷ 12 by Alternatively,
moving the decimal point to the right in both the
moving the decimal pointStep
to the
in both
dividend
dividend and85
divisor. Alternatively, rewrite the problems as:
rewrite the problems
as:
85
Step 2. When performing long division,
the decimal
the
directly above
place
0.48 point
 12in
.8 quotient
Step 2. When performing long division,
place the1.2
decimal
point
in4the
quotient directly above
the decimal point in the dividend.
Continuing the example:
the decimal point in the dividend. Continuing the example:
.
.
12 4.8
12 4.8
85
Step 3. Divide the equation as if it were a whole number. Continuing the example:
Step 3. Divide the equation as if it were a whole number. Continuing the example:
Step 3.
.4
.4
12 4.8
12 4.8
– 4.8
4.8
0
0
Step 2.
ractice
ractice problems
problems
olutions
problems
olutions to
to the
the practice
practice
problems are
are located
located in
in the
the back
back of
of this
this book.
book.
60
Compute the product of 6.3 and 7.6.
Compute the product of 6.3 and 7.6.
TEAS® STUDY MANUAL
MATHEMATICS
Practice problems
Solutions to the practice problems are located in the back of this book.
1. Compute the product of 6.3 and 7.6.
2. Divide 0.05 into 0.710.
3. Simplify the expression: 0.3 × 0.12.
4. Simplify the expression: 0.4 ÷ 0.02.
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