Basic Mathematics for College Students

4.3 Multiplying Decimals 351

7 Estimate products of decimals.

Estimation can be used to check the reasonableness of an answer to a decimal
multiplication. There are several ways to estimate, but the objective is the same: Simplify
the numbers in the problem so that the calculations can be made easily and quickly.

EXAMPLE 11

a.Estimate using front-end rounding:

b.Estimate by rounding each factor to the nearest tenth:

c.Estimate by rounding:

StrategyWe will use rounding to approximate the factors. Then we will find the
product of the approximations.

WHYRounding produces factors that contain fewer digits. Such numbers are
easier to multiply.

Solution
a.To estimate by front-end rounding, we begin by rounding both factors
to their largestplace value.

The estimate is 180. If we calculate , the product is exactly 173.07. The

estimate is close: It’s about 7 more than 173.07.

b.To estimate , we will round both decimals to the nearest tenth.

The estimate is 73.67. If we calculate , the product is exactly

73.3057. The estimate is close: It’s just slightly more than 73.3057.

c.Since 101.4 is approximately 100, we can estimate using

.

Since 100 has twozeros, move the decimal point in

0.1245 twoplaces to the right.

0.1245(100)12.45

0.1245( 100 )

0.1245(101.4)

13.915.27

Round to the nearest tenth.

Round to the nearest tenth.

13.9

 5.3

417

6950

73.67

13.91

 5.27

13.915.27

27 6.41

Round to the nearest ten.

Round to the nearest one.

30

 6

180

27

 6.41

27 6.41

0.1245(101.4)

13.915.27

27 6.41

Self Check 11

a.Estimate using front-end

rounding:

b.Estimate by rounding the

factors to the nearest tenth:

c.Estimate by rounding:

Now TryProblems 61 and 63

0.7899(985.34)

3.09211.642

4.337 65

The estimate is 12.45. If we calculate , the product is exactly

12.6243. Note that the estimate is close: It’s slightly less than 12.6243.

0.1245(101.4)

8 Solve application problems by multiplying decimals.

Application problems that involve repeated addition are often more easily solved
using multiplication.

EXAMPLE (^12) Coins Banks wrap pennies in rolls of 50 coins. If a penny
is 1.55 millimeters thick, how tall is a stack of 50 pennies?
Analyze

• There are 50 pennies in a stack. Given


• A penny is 1.55 millimeters thick. Given


• How tall is a stack of 50 pennies? Find

Self Check 12

COINSBanks wrap nickels in

rolls of 40 coins. If a nickel is

1.95 millimeters thick, how tall

is a stack of 40 nickels?

Now TryProblem 97

Cookey/Dreamstime.com