decimal place

decimal place

A

decimal place

of a number (a real number)

r

is the position of a digit in its

decimal expansion

relative to the

decimal point

. Let us write

r

as a

decimal number

:

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⁢

@

⁢

C

=

0

⁢

p

⁢

t

⁢

@

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H

=

10

⁢

p

⁢

t

⁢

A

n

⁢

A

n

-

1

⁢

…

⁢

A

1

⁢

&

∙

&

⁢

D

1

⁢

D

2

⁢

…

⁢

D

m

⁢

…

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&

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⁢

t

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i

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t

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\restore

⁢

\ar

⁢

[

u

]

⁢

&

where each of the

A

i

and

D

j

is a digit in the decimal system (one of

0

,

1

,

2

,

3

,

4

,

5

,

6

,

7

,

8

,

9

). In this decimal expansion,

•

the

i

-th decimal place to the left of the decimal point is the position of

A

i

, and

•

the

j

-th decimal place to the right of the decimal place is the position of

D

j

.

The digits

A

i

and

D

j

are called the

decimal place values

.

A

i

is the decimal place value corresponding to the

i

-th decimal place to the left of the decimal point, while

D

j

is the decimal place value corresponding to the

j

-th decimal place to the right of the decimal point.

For decimal places closer to the decimal point, specific names are used. Below are some of the most commonly used names:

name

position from

direction from

example

the decimal point

the decimal point

(position of 7)

ones

1st

left

7.2

tens

2nd

left

71

(

=

71.0

)

hundreds

3rd

left

735

(

=

735.0

)

thousands

4th

left

7126

(

=

7126.0

)

tenths

1st

right

0.7

hundredths

2nd

right

12.47

thousandths

3rd

right

9.837

ten thousandths

4th

right

6.0037

𝐑𝐞𝐦𝐚𝐫𝐤

.

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.

Title

decimal place

Canonical name

DecimalPlace

Date of creation

2013-03-22 17:27:24

Last modified on

2013-03-22 17:27:24

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

12

Author

CWoo (3771)

Entry type

Definition

Classification

msc 00A05

Related topic

MetricSystem

Defines

decimal place value

Defines

hundreds

Defines

thousands

Defines

tenths

Defines

hundredths

Defines

thousandths

Defines

ten thousandths

Generated on Tue Feb 6 22:17:56 2018 by

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