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In the last lesson, you were introduced to decimal numbers. Decimal places change by a factor of 10. For example, lets look at the number 3247.8956 below.3 x 1000thousands2 x 100hundreds4 x 10tens7 x 1ones8 x 0.1tenths9 x 0.01hundredths5 x 0.001thousandths6 x 0.0001ten-thousandthsA decimal number can have a whole-number part and a fractional part.Mixed Number- Expanded Form -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 NumberDecimal52..4.0056Example 2: Write each phrase as a mixed number and as a decimal.phrasemixed numberdecimalfive and three tenths5.300000forty-nine and one hundredth49.010000two hundred sixteen and two hundred thirty-one thousandths 216.231000nine thousand, ten and three hundred fifty-nine ten-thousandths9,010.035900seventy-six thousand, fifty-three and forty-seven hundred-thousandths76,053.000470two hundred twenty-nine thousand and eighty-one millionths 229,000.000081Look 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. Lets 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 NumberFractional PartDecimal6...5625Alternate 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: 0.200Student 3: 0.00002Analysis: Lets use our place value chart to help us analyze this problem. PLACE VALUE AND DECIMALS Student 1 200000. Student 2 0.200 Student 3 0.0000 2 Lets look at the expanded form of each decimal to help us find the correct answer.StudentNumberFractionExpanded FormPhrase1200,000.00000 2 x 100,000two hundred thousand20.20000two hundred thousandths30.00002two 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. Lets look at some more examples.Example 5: Write each phrase as a decimal.phraseanalysisfractiondecimalthree hundred ten thousandths 310 thousandths0.310three hundred ten-thousandths 300 ten-thousandths 0.0300Example 6: Write each phrase as a decimal.phraseanalysisfractiondecimaleight hundred thousandths 800 thousandths0.800eight hundred-thousandths 8 hundred-thousandths 0.00008Example 7: Write each phrase as a decimal.phraseanalysisfractiondecimalseven hundred millionths 700 millionths0.000700seven hundred-millionths 7 hundred-millionths 0.00000007In 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 lets look at some examples in which we write these kinds of decimals using words.Example 8: Write each decimal using words.decimalanalysisphrase0.110 110 thousandthsone hundred ten thousandths0.0100 100 ten-thousandthsone hundred ten-thousandthsExample 9: Write each decimal using words.decimalanalysisphrase0.400400 thousandthsfour hundred thousandths0.000044 hundred-thousandthsfour hundred-thousandthsExample 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 millionthsSummary: 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.ExercisesIn 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? 4.Which of the following is equal to 9,? 5.Which of the following is equal to five hundred-thousandths?
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