Basic Mathematics for College Students

4.3 Multiplying Decimals 345

WHYSince the factor 5.9 has 1 decimal place, and the factor 3.4 has 1 decimal
place, the product should have decimal places.

SolutionWe write the multiplication in vertical form and proceed as follows:

Vertical form

Move 2 places from the right to the left

and insert a decimal point in the answer.

Thus,5.93.420.06.



The answer will have

1  1 2 decimal places.

v

1 decimal place

1 decimal place

5.9

 3.4

236

1770

20.06

1  1  2

The Language of Mathematics Recall the vocabulary of multiplication.

Factor

Factor

vPartial products

Product

5.9

 3.4

236

1770

20.06

Success Tip When multiplying decimals, we do not need to line up the

decimal points, as the next example illustrates.

EXAMPLE (^2) Multiply: 1.3(0.005)
StrategyWe will ignore the decimal points and multiply 1.3 and 0.005 as if they
were whole numbers. Then we will write a decimal point in that result so that the
final answer has four decimal places.
WHYSince the factor 1.3 has 1 decimal place, and the factor 0.005 has 3 decimal
places, the product should have decimal places.
SolutionSince many students find vertical form multiplication of decimals easier
if the decimal with the smaller number of nonzero digits is written on the bottom,
we will write 0.005 under 1.3.
Write 2 placeholder zeros in front of 6. Then move 4 places from
the right to the left and insert a decimal point in the answer.
Thus,1.3(0.005)0.0065.

The answer will have
v 1  3 4 decimal places.
1 decimal place
3 decimal places

1.3

 0.005

0. 0065

1  3  4

Self Check 2

Multiply: (0.0002)7.2

Now TryProblem 13

EXAMPLE (^3) Multiply: 234(5.1)
StrategyWe will ignore the decimal point and multiply 234 and 5.1 as if they were
whole numbers. Then we will write a decimal point in that result so that the final
answer has one decimal place.
WHYSince the factor 234 has 0 decimal places, and the factor 5.1 has 1 decimal
place, the product should have 0  1  1 decimal place.
Self Check 3
Multiply: 178(4.7)
Now TryProblem 17