In the critical lesson, you were introduced to decimal numbers. Decimal places readjust by a variable of 10. For example, let"s look at the number "3247.8956" below.

You are watching: Three and fifty four thousandths in decimal form

3 x 1000thousands
2 x 100hundreds
4 x 10tens
7 x 1ones
8 x 0.1tenths
9 x 0.01hundredths
5 x 0.001thousandths
6 x 0.0001ten-thousandths

A decimal number deserve to have a whole-number part and a fountain part.

Mixed Number- Expanded form -Decimal Form
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= (5 x 10) + ( 7 x 1) + (4 x 
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) + (9 x 
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)
= 57.49
 - whole-number component -- fractional part - 

In this lesson, you will certainly learn just how to read and write decimals. You may use our Place Value and also Decimals Chart (PDF) together a visual recommendation for the instances presented in this lesson.

Example 1: compose each combined number as a decimal.

Mixed NumberDecimal
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52.3000
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973.4100
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31.2670
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1842.0056

Example 2: create each expression as a combined number and as a decimal.

phrasemixed numberdecimal
five and three tenths
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5.300000
forty-nine and also one hundredth
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49.010000
two hundred sixteen and also two hundreds thirty-one thousandths
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216.231000
nine thousand, ten and also three hundred fifty-nine ten-thousandths
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9,010.035900
seventy-six thousand, fifty-three and forty-seven hundred-thousandths
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76,053.000470
two hundred twenty-nine thousand and eighty-one millionths
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 229,000.000081

Look at the mixed numbers in the instances above. Girlfriend will an alert that the denominator of the fractional part is a aspect of 10, making it is basic 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 combined number together a decimal.

Analysis: A fraction bar tells us to divide. In order to execute this, we must transform or readjust the fractional part of each blended number to decimal digits. Us will perform this by separating the numerator of each fraction by its denominator.

Mixed NumberFractional PartDecimal
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*
6.9000
*
*
9.7200
*
*
167.1250
*
*
149.5625
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Alternate Method: It should be detailed that some of the fractions above could have actually been converted to decimals using equivalent fractions. Because that example:

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Example 4: When asked to write two hundred thousandths as a decimal, 3 students gave three various answers as displayed below. I beg your pardon student had the correct answer?

Student 1: 200,000.

Student 2: 0.200

Student 3: 0.00002

Analysis: Let"s usage our place value chart to aid us analyze this problem.

 PLACE VALUE and DECIMALS
 
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*
*
 
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*
 
*
*
 
*
*
 
*
*
 
 
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Student 1 200000.      
Student 2      0.200   
Student 3      0.0000 2 
 

Let"s look in ~ the expanded kind of every decimal to aid us uncover the exactly answer.

StudentNumberFractionExpanded FormPhrase
1200,000.00000 2 x 100,000two hundreds thousand
20.20000
*
*
two hundred thousandths
30.00002
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two hundred-thousandths
 

Answer: Thus, two hundred thousandths is 0.200, so student 2 had actually the exactly answer.

As you can see, decimal are called by the ar of the critical digit. Notice that in instance 4, the answer provided by student 3 was two hundred-thousandths. This phrase has actually a hyphen in it. The hyphen is an essential piece of info that helps us read and write decimals. Let"s look in ~ some much more examples.

Example 5: Write each expression as a decimal.

phraseanalysisfractiondecimal
three hundred ten thousandths 310 thousandths
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0.310
three hundred ten-thousandths 300 ten-thousandths
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0.0300

Example 6: compose each expression as a decimal.

phraseanalysisfractiondecimal
eight hundreds thousandths 800 thousandths
*
0.800
eight hundred-thousandths 8 hundred-thousandths
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0.00008

Example 7: compose each expression as a decimal.

phraseanalysisfractiondecimal
seven hundreds millionths 700 millionths
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0.000700
seven hundred-millionths 7 hundred-millionths
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0.00000007

In examples 5 with 7, us were inquiry to write phrases together decimals. Some of the indigenous in the phrase indicate the place-value positions, and other indigenous in the phrase indicate the number to it is in used. Currently let"s look at some examples in i m sorry we compose these kinds of decimals utilizing words.

Example 8: create each decimal utilizing words.

decimalanalysisphrase
0.110 110 thousandthsone hundred ten thousandths
0.0100 100 ten-thousandthsone hundreds ten-thousandths

Example 9: compose each decimal utilizing words.

decimalanalysisphrase
0.400400 thousandthsfour hundreds thousandths
0.000044 hundred-thousandthsfour hundred-thousandths

 

Example 10: Write the following decimal making use of words. Roll your computer mouse over every digit because that help.
  
 
*

 

Answer: The decimal 1,729,405.008365 is composed as:

one million, 7 hundred twenty-nine thousand, four hundred five and eight thousand, three hundred sixty-five millionths

Summary: You learned exactly how to read and also write decimals in this lesson. Once writing a blended number as a decimal, the fractional component must be convert to decimal digits. Decimals are named by the location of the critical digit. The hyphen is an important indicator as soon as reading and also writing decimals. Once writing a expression as a decimal, few of the words indicate the place-value positions, and also other words indicate the number to it is in used.

Exercises

In exercises 1 and also 2, click when in response BOX and kind in your answer; then click ENTER. After friend click ENTER, a message will appear in the results BOX to show whether your answer is correct or incorrect. To start over, click CLEAR.

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prize BOX:   

results BOX: 

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prize BOX:   

results BOX: 

In exercises 3 with 5, review each inquiry below. Choose your prize by clicking on its button. Feedback to her answer is noted in the outcomes BOX. If you make a mistake, pick a various button.
3.Which that the following is equal to seven hundred 5 thousand and eighty-nine ten-thousandths?
 700.005.089705,000.089705,000.0089705,000.00089

RESULTS BOX: 

4.Which that the complying with is equal to 9,842.1039?
 nine thousand, eight hundred, fourty two and also one thousand, thirty-nine millionthsnine thousand, eight hundred, forty-two and also one thousand, thirty-nine ten-thousandthsnine thousand, eight hundred, forty-two and also one thousand, thirty-nine thousandthsNone the the above.

See more: What Does It Mean When A Man Calls You My Dear, What Does It Mean When A Guy Calls You Dear

RESULTS BOX: 

5.Which of the complying with is equal to five hundred-thousandths?
 500,0000.5000.00050.00005

RESULTS BOX: