Algebra Demystified 2nd Ed

Chapter 3 DeCiMalS 69

6. 0.446 + 1.2
   0 446
   1 200
   1 646

+

7. 2.99 + 3
   299
   300
   599

+

Multiplying Decimal Numbers

To multiply decimal numbers, we perform multiplication, ignoring the decimal
point, and then we decide where to put the decimal point. We count the num-
ber of digits that follow the decimal points in the factors. This total will be the
number of digits that follow the decimal point in the product.

EXAMPLES

Find the product.

12.83 · 7.91 The product has four digits following the decimal point.

1283 791⋅  ,= 1 014 853, , so 12.83 · 7.91 = 101.4853

3.782 · 19.41 The product has five digits following the decimal point.

3782 1941⋅  =  7340862 , so 3.782 · 19.41 = 73.40862

14 · 3.55 The product has two digits following the decimal point.

14 355⋅  =  4970 , so 14 · 3.55 = 49.70

To see why this strategy works, let us compute 14 51..× 2 after writing these
numbers as fractions.

14 51 2 14

10

512

1000

14 512

10 100

7168

1000

.. () 7

()

⋅=⋅= ==..168

Because the denominator of the final fraction is 1000 (1 followed by three 0s),
we move the decimal place three places.

PRACTICE

Find the product.

1. 3.2 · 1.6 =


2. 4.11 · 2.84 =

EXAMPLES

Find the product.

PRACTICE

Find the product.