Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Fundamentals of Mathematics » Reading and Writing Decimals

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • CCQ display tagshide tags

    This collection is included in aLens by: Community College of Qatar

    Comments:

    "Used as supplemental materials for developmental math courses."

    Click the "CCQ" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

  • College Open Textbooks display tagshide tags

    This collection is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook Collaborative

    Comments:

    "Reviewer's Comments: 'I would recommend this text for a basic math course for students moving on to elementary algebra. The information in most chapters is useful, very clear, and easily […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "Fundamentals of Mathematics is a work text that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • UniqU content

    This collection is included inLens: UniqU's lens
    By: UniqU, LLC

    Click the "UniqU content" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Reading and Writing Decimals

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to read and write decimals. By the end of the module students should understand the meaning of digits occurring to the right of the ones position, be familiar with the meaning of decimal fractions and be able to read and write a decimal fraction.

Section Overview

  • Digits to the Right of the Ones Position
  • Decimal Fractions
  • Reading Decimal Fractions
  • Writing Decimal Fractions

Digits to the Right of the Ones Position

We began our study of arithmetic ((Reference)) by noting that our number system is called a positional number system with base ten. We also noted that each position has a particular value. We observed that each position has ten times the value of the position to its right.

10 times 100,000 is the millions position. 10 times 10,000 is the hundred thousands position. 10 times 1,000 is the ten thousands position. 10 times 100 is the thousands position. 10 times 10 is the hundreds position. 10 times 1 is the tens position. 1 is the ones position.

This means that each position has 110110 the value of the position to its left.

1,000,000 is the millions position. One tenth of 1,000,000 is the hundred thousands. One tenths of 100,000 is the ten thousands. One tenth of 10,000 is the thousands position. One tenth of 1,000 is the thousands. One tenth of 100 is the tens position. One tenth of 10 is the ones position.

Thus, a digit written to the right of the units position must have a value of 110110 size 12{ { {1} over {"10"} } } {} of 1. Recalling that the word "of" translates to multiplication ⋅⋅, we can see that the value of the first position to the right of the units digit is 110110 size 12{ { {1} over {"10"} } } {} of 1, or

1 10 ⋅ 1 = 1 10 1 10 ⋅ 1 = 1 10 size 12{ { {1} over {"10"} } cdot 1= { {1} over {"10"} } } {}

The value of the second position to the right of the units digit is 110110 size 12{ { {1} over {"10"} } } {} of 110110 size 12{ { {1} over {"10"} } } {}, or

1 10 ⋅ 1 10 = 1 10 2 = 1 100 1 10 ⋅ 1 10 = 1 10 2 = 1 100 size 12{ { {1} over {"10"} } cdot { {1} over {"10"} } = { {1} over {"10" rSup { size 8{2} } } } = { {1} over {"100"} } } {}

The value of the third position to the right of the units digit is 110110 size 12{ { {1} over {"10"} } } {} of 11001100 size 12{ { {1} over {"100"} } } {}, or

1 10 ⋅ 1 100 = 1 10 3 = 1 1000 1 10 ⋅ 1 100 = 1 10 3 = 1 1000 size 12{ { {1} over {"10"} } cdot { {1} over {"10"} } = { {1} over {"10" rSup { size 8{3} } } } = { {1} over {"1000"} } } {}

This pattern continues.

We can now see that if we were to write digits in positions to the right of the units positions, those positions have values that are fractions. Not only do the positions have fractional values, but the fractional values are all powers of 10 10,102,103,…10,102,103,… size 12{ left ("10","10" rSup { size 8{2} } ,"10" rSup { size 8{3} } , dotslow right )} {}.

Decimal Fractions

Decimal Point, Decimal

If we are to write numbers with digits appearing to the right of the units digit, we must have a way of denoting where the whole number part ends and the fractional part begins. Mathematicians denote the separation point of the units digit and the tenths digit by writing a decimal point. The word decimal comes from the Latin prefix "deci" which means ten, and we use it because we use a base ten number system. Numbers written in this form are called decimal fractions, or more simply, decimals.

millions, hundred thousands, ten thousands, thousands, hundreds, tens and ones are to the left of the decimal point. tenths, hundredths, thousandths, ten thousandths, hundred thousandths, and millionths are to the right of the decimal point.

Notice that decimal numbers have the suffix "th."

Decimal Fraction

A decimal fraction is a fraction in which the denominator is a power of 10.

The following numbers are examples of decimals.

  1. 42.6

    The 6 is in the tenths position.

    42 . 6 = 42 6 10 42 . 6 = 42 6 10 size 12{"42" "." 6="42" { {6} over {"10"} } } {}

  2. 9.8014

    The 8 is in the tenths position.
    The 0 is in the hundredths position.
    The 1 is in the thousandths position.
    The 4 is in the ten thousandths position.

    9 . 8014 = 9 8014 10 , 000 9 . 8014 = 9 8014 10 , 000 size 12{9 "." "8014"=9 { {"8014"} over {"10","000"} } } {}

  3. 0.93

    The 9 is in the tenths position.
    The 3 is in the hundredths position.

    0 . 93 = 93 100 0 . 93 = 93 100 size 12{0 "." "93"= { {"93"} over {"100"} } } {}

    Note:

    Quite often a zero is inserted in front of a decimal point (in the units position) of a decimal fraction that has a value less than one. This zero helps keep us from overlooking the decimal point.
  4. 0.7

    The 7 is in the tenths position.

    0 . 7 = 7 10 0 . 7 = 7 10 size 12{0 "." 7= { {7} over {"10"} } } {}

    Note:

    We can insert zeros to the right of the right-most digit in a decimal fraction without changing the value of the number.
    7 10 = 0 . 7 = 0 . 70 = 70 100 = 7 10 7 10 = 0 . 7 = 0 . 70 = 70 100 = 7 10 size 12{ { {7} over {"10"} } =0 "." 7=0 "." "70"= { {"70"} over {"100"} } = { {7} over {"10"} } } {}

Reading Decimal Fractions

Reading a Decimal Fraction

To read a decimal fraction,

  1. Read the whole number part as usual. (If the whole number is less than 1, omit steps 1 and 2.)
  2. Read the decimal point as the word "and."
  3. Read the number to the right of the decimal point as if it were a whole number.
  4. Say the name of the position of the last digit.

Sample Set A

Read the following numbers.

Example 1

6.8

6.8 is six and eight tenths. The 8 is in the tenths position.

Note:
Some people read this as "six point eight." This phrasing gets the message across, but technically, "six and eight tenths" is the correct phrasing.

Example 2

14.116

14.116 is fourteen and one hundred sixteen thousandths. The six is in the thousandths position.

Example 3

0.0019

0.0019 is nineteen ten thousandths. The nine is in the ten thousandths position.

Example 4

81

Eighty-one

In this problem, the indication is that any whole number is a decimal fraction. Whole numbers are often called decimal numbers.

81 = 81 . 0 81 = 81 . 0 size 12{"81"="81" "." 0} {}

Practice Set A

Read the following decimal fractions.

Exercise 1

12.9

Solution

twelve and nine tenths

Exercise 2

4.86

Solution

four and eighty-six hundredths

Exercise 3

7.00002

Solution

seven and two hundred thousandths

Exercise 4

0.030405

Solution

thirty thousand four hundred five millionths

Writing Decimal Fractions

Writing a Decimal Fraction

To write a decimal fraction,

  1. Write the whole number part.
  2. Write a decimal point for the word "and."
  3. Write the decimal part of the number so that the right-most digit appears in the position indicated in the word name. If necessary, insert zeros to the right of the decimal point in order that the right-most digit appears in the correct position.

Sample Set B

Write each number.

Example 5

Thirty-one and twelve hundredths.

The decimal position indicated is the hundredths position.

31.12

Example 6

Two and three hundred-thousandths.

The decimal position indicated is the hundred thousandths. We'll need to insert enough zeros to the immediate right of the decimal point in order to locate the 3 in the correct position.

2.00003

Example 7

Six thousand twenty-seven and one hundred four millionths.

The decimal position indicated is the millionths position. We'll need to insert enough zeros to the immediate right of the decimal point in order to locate the 4 in the correct position.

6,027.000104

Example 8

Seventeen hundredths.

The decimal position indicated is the hundredths position.

0.17

Practice Set B

Write each decimal fraction.

Exercise 5

Three hundred six and forty-nine hundredths.

Solution

306.49

Exercise 6

Nine and four thousandths.

Solution

9.004

Exercise 7

Sixty-one millionths.

Solution

0.000061

Exercises

For the following three problems, give the decimal name of the posi­tion of the given number in each decimal fraction.

Exercise 8

1. 3.941
9 is in the
position.
4 is in the
position.
1 is in the
position.

Solution

Tenths; hundredths, thousandths

Exercise 9

17.1085
1 is in the
position.
0 is in the
position.
8 is in the
position.
5 is in the
position.

Exercise 10

652.3561927
9 is in the
position.
7 is in the
position.

Solution

Hundred thousandths; ten millionths

For the following 7 problems, read each decimal fraction by writing it.

Exercise 11

9.2

Exercise 12

8.1

Solution

eight and one tenth

Exercise 13

10.15

Exercise 14

55.06

Solution

fifty-five and six hundredths

Exercise 15

0.78

Exercise 16

1.904

Solution

one and nine hundred four thousandths

Exercise 17

10.00011

For the following 10 problems, write each decimal fraction.

Exercise 18

Three and twenty one-hundredths.

Solution

3.20

Exercise 19

Fourteen and sixty seven-hundredths.

Exercise 20

One and eight tenths.

Solution

1.8

Exercise 21

Sixty-one and five tenths.

Exercise 22

Five hundred eleven and four thousandths.

Solution

511.004

Exercise 23

Thirty-three and twelve ten-thousandths.

Exercise 24

Nine hundred forty-seven thousandths.

Solution

0.947

Exercise 25

Two millionths.

Exercise 26

Seventy-one hundred-thousandths.

Solution

0.00071

Exercise 27

One and ten ten-millionths.

Calculator Problems

For the following 10 problems, perform each division using a calculator. Then write the resulting decimal using words.

Exercise 28

3÷43÷4 size 12{3¸4} {}

Solution

seventy-five hundredths

Exercise 29

1÷81÷8 size 12{1¸8} {}

Exercise 30

4÷104÷10 size 12{4¸"10"} {}

Solution

four tenths

Exercise 31

2÷52÷5 size 12{2¸5} {}

Exercise 32

4÷254÷25 size 12{4¸"25"} {}

Solution

sixteen hundredths

Exercise 33

1÷501÷50 size 12{1¸"50"} {}

Exercise 34

3÷163÷16 size 12{3¸"16"} {}

Solution

one thousand eight hundred seventy-five ten thousandths

Exercise 35

15÷815÷8 size 12{"15"¸8} {}

Exercise 36

11÷2011÷20 size 12{"11"¸"20"} {}

Solution

fifty-five hundredths

Exercise 37

9÷409÷40 size 12{9¸"40"} {}

Exercises for Review

Exercise 38

((Reference)) Round 2,614 to the nearest ten.

Solution

2610

Exercise 39

((Reference)) Is 691,428,471 divisible by 3?

Exercise 40

((Reference)) Determine the missing numerator.

3 14 = ? 56 3 14 = ? 56 size 12{ { {3} over {14} } = { {?} over {"56"} } } {}

Solution

12

Exercise 41

((Reference)) Find 316 of 3239316 of 3239 size 12{ { {3} over {"16"} } " of " { {"32"} over {"39"} } } {}

Exercise 42

((Reference)) Find the value of 2581+232+192581+232+19 size 12{ sqrt { { {"25"} over {"81"} } } + left ( { {2} over {3} } right ) rSup { size 8{2} } + { {1} over {9} } } {}

Solution

109   or   119109   or   119 size 12{ { {"10"} over {9} } " or "1 { {1} over {9} } } {}

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks