Read and Write
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.
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