Basic Mathematics for College Students

396 Chapter 4 Decimals

To compare two decimals:

1.Make sure both numbers have the same

number of decimal places to the right of the

decimal point. Write any additional zeros

necessary to achieve this.

2.Compare the digits of each decimal, column by

column, working from left to right.

3.If the decimals are positive: When two digits

differ, the decimal with the greater digit is the

greater number.

If the decimals are negative: When two digits

differ, the decimal with the smaller digit is the

greater number.

Compare 47.31572 and 47.31569.

47.315 7 2

47.315 6 9

As we work from left to right, this is the first column in

which the digits differ. Since 7 6, it follows that

47.31572 is greater than 47.31569.

Thus,.

Compare and.

6.41 8 These decimals are negative.

6.41 0 Write a zero after 1 to help in the comparison.

As we work from left to right, this is the first column in

which the digits differ. Since 0 8, it follows that 6.410

is greater than 6.418.

Thus,6.416.418.

6.418 6.41

47.3157247.31569

To graph a decimal number means to make a

drawing that represents the number.

Graph , 0.6, , 3.99, and on a number line.

− 5 − 4 − 3 − 2 −10 12 34 5

–2.89–2.17–0.50.6 3.99

2.17 2.89 0.5

1.To round a decimalto a certain decimal place

value, locate the rounding digitin that place.

2.Look at the test digitdirectly to the right of the

rounding digit.

3.If the test digit is 5 or greater, round up by

adding 1 to the rounding digit and dropping all

the digits to its right. If the test digit is less than

5, round down by keeping the rounding digit

and dropping all the digits to its right.

Round 33.41632 to the nearest thousandth.

Rounding digit: Keep the rounding digit:

thousandths column Do not add 1.

33.41632 33.41632

Test digit: 3 is less than 5. Drop the test digit and all

digits to its right.

Thus, 33.41632 rounded to the nearest thousandth is 33.416.

Round 2.798 to the nearest hundredth.

Rounding digit: Add 1. Since 9  1 10,

hundredths column write 0 in this column and

carry 1 to the tenths column.

2.798

Test digit: 8 is 5 or greater. Drop the test digit.

Thus, 2.798 rounded to the nearest hundredth is 2.80.

2.7

1

98

There are many situations in our daily lives that

call for rounding amounts of money.

Rounded to the nearest cent,$0.14672 is $0.15.

Rounded to the nearest dollar,$142.39 is $142.

REVIEW EXERCISES

1. a.Represent the amount of
   the square region that is
   shaded, using a decimal
   and a fraction.
   b. Shade 0.8 of the region
   shown below.


2. Consider the decimal number 2,809.6735.
   a. What is the place value of the digit 7?
   b. Which digit tells the number of thousandths?
   c. Which digit tells the number of hundreds?
   d. What is the place value of the digit 5?


3. Write 16.4523 in expanded notation.