Basic Mathematics for College Students

The decimal 365.24219, entered in the place-value chart above, represents the
number of days it takes Earth to make one full orbit around the sun. We say that the
decimal is written in standard form(also called standard notation). Each of the 2’s in

365. 242 19 has a different place value because of its position. The place value of the red
     2 is two tenths. The place value of the blue 2 is two thousandths.

4.1 An Introduction to Decimals 317

35.2 6

Decimal point

Ten

Tens ths

Hundreds

4129

Million

ths

Hundred-thousand

ths

Ten-thousand

ths

Hundred

ths

Thousands Ones

Hundred thousandsTen thousands

Millions Thousand

ths

Whole-number part Fractional part

Sun

Earth

EXAMPLE (^1) Consider the decimal number: 2,864.709531
a.What is the place value of the digit 5?
b.Which digit tells the number of millionths?
StrategyWe will locate the decimal point in 2,864.709531. Then, moving to the
right, we will name each column (tenths, hundredths, and so on) until we reach 5.
WHYIt’s easier to remember the names of the columns if you begin at the
decimal point and move to the right.
Solution
a.2,864.709 531 Say “Tenths, hundredths, thousandths, ten-thousandths” as you
move from column to column.
5 ten-thousandths is the place value of the digit 5.
b.2,864.70953 1 Say “Tenths, hundredths, thousandths, ten-thousandths, hundred
thousandths, millionths” as you move from column to column.
The digit 1 is in the millionths column.


Self Check 1
Consider the decimal number:
56,081.639724
a.What is the place value of the
digit 9?
b.Which digit tells the number
of hundred-thousandths?
Now TryProblem 17
We can write a whole number in decimal notation by placing a decimal point
immediately to its right and then entering a zero, or zeros, to the right of the decimal
point. For example,
Because
A whole number Place a decimal point here and enter
a zero, or zeros, to the right of it.
When there is no whole-number part of a decimal, we can show that by entering
a zero directly to the left of the decimal point. For example,
Because
No whole-number part Enter a zero here, if desired.
Negative decimals are used to describe many situations that arise in everyday life,
such as temperatures below zero and the balance in a checking account that is
overdrawn. For example, the coldest natural temperature ever recorded on Earth was
128.6°Fat the Russian Vostok Station in Antarctica on July 21, 1983.
83
100 ^0
83
.83  0.83 100.

99  99.0  99.00 99  99 100  99 10000.

©Topham/The Image Works. Reproduced bypermission

  

 

Caution! We do notseparate groups of three digits on the right side of the

decimal point with commas as we do on the left side. For example, it would be

incorrect to write:

2,864.709,531