4.3 Multiplying Decimals 349b.
Write 1 billion in standard form.
Since 1,000,000,000 has ninezeros, move
the decimal point in 14.63 nineplaces to the
right.
c.
Write 1 trillion in standard form.
Since 1,000,000,000,000 has twelvezeros,
move the decimal point in 5.9 twelveplaces to
the right.5,900,000,000,000
5.91,000,000,000,000
5.9 trillion5.91 trillion14,630,000,000
14.631,000,000,000
14.63 billion14.631 billion3 Multiply signed decimals.
The rules for multiplying integers also hold for multiplying signed decimals. The
product of two decimals with like signs is positive, and the product of two decimals
with unlike signs is negative.
EXAMPLE (^7) Multiply: a. b.
StrategyIn part a, we will use the rule for multiplying signed decimals that have
different (unlike) signs. In part b, we will use the rule for multiplying signed
decimals that have the same (like) signs.
WHYIn part a, one factor is negative and one is positive. In part b, both factors are
negative.
Solution
a.Find the absolute values: and. Since the decimals
have unlike signs, their product is negative.
Multiply the absolute values, 1.8 and 4.5, to get 8.1.
Then make the final answer negative.
b.Find the absolute values: and. Since the
decimals have like signs, their product is positive.
59,080
Multiply the absolute values, 1,000 and
59.08. Since 1,000 has 3 zeros, move
the decimal point in 59.08 3 places to
the right. Write a placeholder zero. The
answer is positive.(1,000)(59.08)1,000(59.08)
0 1,000 0 1,000 0 59.08 0 59.08
1.8(4.5)8.1
0 1.8 0 1.8 0 4.5 0 4.5
1.8(4.5) (1,000)(59.08)
Self Check 7
Multiply:
a.
b.
Now TryProblems 37 and 4144.968(100)
6.6(5.5)
4 Evaluate exponential expressions that have decimal bases.
We have evaluated exponential expressions that have whole number bases, integer
bases, and fractional bases. The base of an exponential expression can also be a
positive or a negative decimal.
1.8
4.5
90
720
8.10EXAMPLE (^8) Evaluate: a.(2.4) (^2) b.
StrategyWe will write each exponential expression as a product of repeated
factors, and then perform the multiplication. This requires that we identify the base
and the exponent.
WHYThe exponent tells the number of times the base is to be written as a factor.
(0.05)^2
Self Check 8
Evaluate:
a.
b.(0.09)^2
Now TryProblems 45 and 47(1.3)^2