
Read and Write
Decimals 

Unit 12 > Lesson 2 of 12 
In the last lesson, you were introduced to decimal numbers. Decimal places change by a factor of 10. For example, let's look at the number
3,247.8956 below.

3 
x 
1000 
thousands 
2 
x 
100 
hundreds 
4 
x 
10 
tens 
7 
x 
1 
ones 
8 
x 
0.1 
tenths 
9 
x 
0.01 
hundredths 
5 
x 
0.001 
thousandths 
6 
x 
0.0001 
tenthousandths 
A decimal number can have a wholenumber part and a fractional part.
Mixed Number 
 E x p a n d e d F
o r m  
Decimal Form 

= (5 x 10) + ( 7 x 1) 
+ (4 x )
+ (9 x ) 
= 57.49 

 wholenumber part  
 fractional part  

In this lesson, you
will learn how to read and write decimals. You may use our Place
Value and Decimals Chart (PDF) as a visual reference for the examples
presented in this lesson.

Example 1: Write each mixed number as a decimal.
Mixed Number 
Decimal 

52.3000 

973.4100 

31.2670 

1,842.0056 
Example 2: Write each phrase as a mixed number and as a decimal.
phrase 
mixed number 
decimal 
five and three tenths 

5.300000 
fortynine and one hundredth 

49.010000 
two hundred sixteen and two hundred thirtyone thousandths 

216.231000 
nine thousand, ten and three hundred fiftynine tenthousandths 

9,010.035900 
seventysix thousand, fiftythree and fortyseven hundredthousandths 

76,053.000470 
two hundred twentynine thousand and eightyone millionths 

229,000.000081 
Look at the mixed numbers in the examples above. You will notice that the denominator of the fractional part
is a factor of
10, making it is easy to convert to a decimal. Let's look at some examples
in which the denominator is not a factor of 10.

Example 3: 
Write each mixed number as a decimal. 
Analysis: 
A fraction bar tells us to divide. In order to do this, we must convert
or change the
fractional part of each mixed number to decimal
digits. We will do this by dividing the
numerator of each fraction by its denominator. 



Mixed Number 
Fractional Part 
Decimal 


6.9000 


9.7200 


167.1250 


149.5625 


Alternate Method: 
It should be noted that some of the fractions above could have been converted
to decimals using
equivalent
fractions. For example: 


Example 4: 
When asked to write two hundred thousandths as a decimal, three
students gave three different answers as shown below. Which student had the correct
answer?


Student 1: 

200,000. 
Student 2: 

0.200 
Student 3: 

0.00002 

Analysis: 
Let's use our place value chart to help us analyze this problem.



PLACE
VALUE AND DECIMALS 















Student 1 

2 
0 
0 
0 
0 
0 
. 






Student 2 






0 
. 
2 
0 
0 



Student 3 






0 
. 
0 
0 
0 
0 
2 





Let's look at the expanded form of each decimal to help us find the correct
answer.


Student 
Number 
Fraction 
Expanded Form 
Phrase 
1 
200,000.00000 

2 x 100,000 
two hundred thousand 
2 
0.20000 


two hundred thousandths 
3 
0.00002 


two hundredthousandths 



Answer: 
Thus, two hundred thousandths is 0.200, so Student 2 had the correct
answer.

As you can see, decimals are named by the place of the last digit. Notice that in Example 4, the answer given by Student 3
was two hundredthousandths. This phrase has a hyphen in it. The hyphen is an important piece of information that
helps us read and write decimals. Let's look at some more examples.

Example 5: Write each phrase as a decimal.
phrase 
analysis 
fraction 
decimal 
three hundred ten thousandths 
310 thousandths 

0.310 
three hundred tenthousandths 
300 tenthousandths 

0.0300 
Example 6: Write each phrase as a decimal.
phrase 
analysis 
fraction 
decimal 
eight hundred thousandths 
800 thousandths 

0.800 
eight hundredthousandths 
8 hundredthousandths 

0.00008 
Example 7: Write each phrase as a decimal.
phrase 
analysis 
fraction 
decimal 
seven hundred millionths 
700 millionths 

0.000700 
seven hundredmillionths 
7 hundredmillionths 

0.00000007 
In Examples 5 through 7, we were asked to write phrases as decimals. Some of
the words in the phrase indicate the placevalue positions, and other words
in the phrase indicate the
digits to be used. Now let's look at some examples in which we write these kinds of decimals using words.

Example 8: Write each decimal using words.
decimal 
analysis 
phrase 
0.110 
110 thousandths 
one hundred ten thousandths 
0.0100 
100 tenthousandths 
one hundred tenthousandths 
Example 9: Write each decimal using words.
decimal 
analysis 
phrase 
0.400 
400 thousandths 
four hundred thousandths 
0.00004 
4 hundredthousandths 
four hundredthousandths 
Example 10: 
Write the following decimal using words. Roll your mouse over each digit for help. 




Answer: 
The decimal 1,729,405.008365 is written as: 

one million, seven
hundred twentynine thousand, four hundred five and eight thousand, three hundred
sixtyfive millionths 
Summary: 
You learned how to read and write decimals in this lesson. When writing
a mixed number as a decimal, the fractional part must be converted to
decimal digits. Decimals are named by the place of the last
digit. The
hyphen is an important indicator when reading and writing decimals. When writing a phrase as a decimal, some of
the words indicate the placevalue positions, and other words indicate the
digits to be used.

Exercises
In Exercises 1 and 2, click once
in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to
indicate whether your answer is correct or incorrect. To start over, click CLEAR.

In Exercises 3 through 5, read each question below. Select your answer by
clicking on its button. Feedback to your answer is provided in the RESULTS BOX.
If you make a mistake, choose a different button.

3.

Which of the following is equal to seven hundred
five thousand and eightynine tenthousandths? 



4.

Which of the following is equal to 9,842.1039? 



5.

Which of the following is equal to five hundredthousandths? 



This lesson is by Gisele Glosser. You can find me on Google.
