Basic Mathematics for College Students

When we inspect the answers, the decimal point in the first factor 5.19 appears to

be moved to the left by the multiplication process. The number of places that it moves

depends on the power of ten by which it is multiplied.

These observations illustrate the following rule.

348 Chapter 4 Decimals

Multiplying a Decimal by 0.1, 0.01, 0.001, and So On

To find the product of a decimal and 0.1, 0.01, 0.001, and so on, move the

decimal point to the left the same number of decimal places as there are in the

power of 10.

EXAMPLE (^5) Multiply: a. b.9.76(0.0001)
StrategyFor each multiplication, we will identify the factor of the form 0.1, 0.01,
and 0.001, and count the number of decimal places that it has.
WHYTo find the product of a decimal and a power of 10 that is less than 1, we
move the decimal point to the left the same number of decimal places as there are
in the power of 10.
Solution
a. Since 0.01 has twodecimal places, move the decimal point
in 145.8 twoplaces to the left.
b.9.76(0.0001)0. 000976 Since 0.0001 has fourdecimal places, move the decimal

145.80.011.458

145.80.01

Self Check 5

Multiply:

a.0.1(129.9)

b.

Now TryProblems 25 and 27

0.0020.00001

point in 9.76 fourplaces to the left. This requires that

three placeholder zeros (shown in blue) be inserted in front

of the 9.



Quite often, newspapers, websites, and television programs present large numbers

in a shorthand notation that involves a decimal in combination with a place-value

column name. For example,

• As of December 31, 2008, Sony had sold 21.3 millionPlaystation 3 units
  worldwide. (Source: Sony Computer Entertainment)


• Boston’s Big Dig was the most expensive single highway project in U.S.
  history. It cost about $14.63 billion.(Source: Roadtraffic-technology.com)


• The distance that light travels in one year is about 5.878 trillionmiles.
  (Source: Encyclopaedia Britannica)
  We can use the rule for multiplying a decimal by a power of ten to write these
  large numbers in standard form.

EXAMPLE (^6) Write each number in standard notation:
a.21.3 million b.14.63 billion c.5.9 trillion
StrategyWe will express each of the large numbers as the product of a decimal
and a power of 10.
WHYThen we can use the rule for multiplying a decimal by a power of 10 to find
their product. The result will be in the required standard form.
Solution
a.
Write 1 million in standard form.
Since 1,000,000 has sixzeros, move the
decimal point in 21.3 sixplaces to the right.

21,300,000

21.31,000,000

21.3 million21.31 million

Self Check 6

Write each number in standard

notation:

a.567.1 million

b.50.82 billion

c.4.133 trillion

Now TryNow Try Problems 29, 31,

and 33