Reading and Writing Decimals

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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.

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: