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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 ten-thousandths

A decimal number can have a whole-number 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
  ---- whole-number 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
forty-nine and one hundredth 49.010000
two hundred sixteen and two hundred thirty-one thousandths     216.231000
nine thousand, ten and three hundred fifty-nine ten-thousandths     9,010.035900
seventy-six thousand, fifty-three and forty-seven hundred-thousandths 76,053.000470
two hundred twenty-nine thousand and eighty-one 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 hundred-thousandths
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 hundred-thousandths. 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 ten-thousandths  300 ten-thousandths   0.0300

Example 6: Write each phrase as a decimal.

phrase analysis fraction decimal
eight hundred thousandths  800 thousandths 0.800
eight hundred-thousandths  8 hundred-thousandths   0.00008

Example 7: Write each phrase as a decimal.

phrase analysis fraction decimal
seven hundred millionths  700 millionths 0.000700
seven hundred-millionths  7 hundred-millionths   0.00000007

In Examples 5 through 7, we were asked to write phrases as decimals. Some of the words in the phrase indicate the place-value 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 ten-thousandths one hundred ten-thousandths

Example 9: Write each decimal using words.

decimal analysis phrase
0.400 400 thousandths four hundred thousandths
0.00004 4 hundred-thousandths four hundred-thousandths

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 twenty-nine thousand, four hundred five and eight thousand, three hundred sixty-five 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 place-value 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.

    ANSWER BOX:

    RESULTS BOX:


     ANSWER BOX:

     RESULTS BOX:


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 eighty-nine ten-thousandths?
 
700.005.089
705,000.089
705,000.0089
705,000.00089

RESULTS BOX:



4. Which of the following is equal to 9,842.1039?
 
nine thousand, eight hundred, forty two and one thousand, thirty-nine millionths
nine thousand, eight hundred, forty-two and one thousand, thirty-nine ten-thousandths
nine thousand, eight hundred, forty-two and one thousand, thirty-nine thousandths
None of the above.

RESULTS BOX:



5. Which of the following is equal to five hundred-thousandths?
 
500,000
0.500
0.0005
0.00005

RESULTS BOX:




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

Lessons on Decimals, Part I
Introduction
Reading and Writing Decimals
Comparing Decimals
Ordering Decimals
Estimating Decimal Sums
Adding Decimals
Estimating Decimal Differences
Subtracting Decimals
Solving Decimal Word Problems
Practice Exercises
Challenge Exercises
Solutions

Related Activities
Interactive Puzzles
Printable Worksheets
Percent Goodies Game

Need More Practice?
Try our Decimal Worksheet Generator
Try our Money Worksheet Generator
Try our Place Value Worksheet Generator


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