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 '3247.8956' 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   Expanded Form   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  
1842.0056 
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.


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.


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


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? 