Basic Mathematics for College Students

The place values of the columns for the fractional part of a decimal are 101 , 1001 ,

318 Chapter 4 Decimals

2 Write decimals in expanded form.

The decimal 4.458, entered in the place-value chart below, represents the time (in

seconds) that it took women’s record holder Melanie Troxel to cover a quarter mile in

her top-fuel dragster. Notice that the place values of the columns for the whole-

number part are 1, 10, 100, 1,000, and so on. We learned in Section 1.1 that the value

of each of those columns is 10 times greater than the column directly to its right.

The Language of Mathematics The word decimalcomes from the Latin

word decima,meaning a tenth part.

EXAMPLE (^2) Write the decimal number 592.8674 in expanded form.
StrategyWorking from left to right, we will give the place value of each digit and
combine them with symbols.
WHYThe term expanded formmeans to write the number as an addition of the
place values of each of its digits.
SolutionThe expanded form of 592.8674 is:
which can be written as

500  90  2 

8

10



6

100



7

1,000



4

10,000

5 hundreds 9 tens 2 ones 8 tenths 6 hundredths 7 thousandths 4 ten-thousandths



Self Check 2

Write the decimal number

1,277.9465 in expanded form.

Now TryProblems 23 and 27

© Les Welch/Icon SMI/Corbis

4.4

Decimal point

Ten

ths

HundredsTens

5 8

Hu

ndred-thousand

ths

Ten-thousand

ths

Hundred

ths

Ones

Ten thousandsThousands

Hundred thousands

Thousand

ths

Whole-number part

100,000 10,0001,000 100 10 1 –– 101 100 –––^1 1,000––––^1 –––––10,000^1 100,000––––––^1

Fractional part

and so on. Each of those columns has a value that is of the value of the place

directly to its left. For example,

• The value of the tenths column is of the value of the ones column:


• The value of the hundredths column is of the value of the tenths column:


• The value of the thousandths column is of the value of the hundredths
  column:
  The meaning of the decimal 4.458 becomes clear when we write it in expanded
  form(also called expanded notation).

which can be written as:

4.458 4 

4

10



5

100



8

1,000

4.458 4 ones 4 tenths 5 hundredths 8 thousandths

1

100 

1

10 

1

1,000^.

1

10

1

10 

1

10 

1

100.

1

10

101 1  101  101.

1

10

1

1,000^ ,