In the last lesson, girlfriend were introduced to decimal numbers. Decimal places readjust by a element of 10. For example, let"s look in ~ the number "3247.8956" below.

You are watching: Six hundred 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 fractional part.

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

In this lesson, you will certainly learn just how to read and write decimals. You may use our Place Value and Decimals Chart (PDF) together a visual reference 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 phrase as a combined number and as a decimal.

phrasemixed numberdecimal
five and also three tenths
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5.300000
forty-nine and also one hundredth
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49.010000
two hundred sixteen and two hundreds thirty-one thousandths
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216.231000
nine thousand, ten and 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 combined numbers in the examples above. You will notification that the denominator of the fractional part is a factor of 10, making the is basic to transform to a decimal. Let"s look in ~ some examples in which the denominator is not a aspect of 10.

Example 3: Write each mixed number together a decimal.

Analysis: A portion bar tells united state to divide. In order to execute this, us must convert or change the fractional part of each mixed number to decimal digits. Us will perform this by splitting the molecule of each portion by that is denominator.

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

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Example 4: When asked come write two hundred thousandths as a decimal, three students gave three different answers as presented below. Which student had actually the correct answer?

Student 1: 200,000.

Student 2: 0.200

Student 3: 0.00002

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

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

Let"s look at the expanded type of each decimal to aid us discover the correct answer.

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

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

As you can see, decimal are named by the place of the last digit. An alert that in instance 4, the answer given by college student 3 was two hundred-thousandths. This phrase has actually a hyphen in it. The hyphen is vital piece of information that helps us read and write decimals. Let"s look in ~ some an ext examples.

Example 5: Write each expression as a decimal.

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

Example 6: write each phrase 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: create each phrase 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 instances 5 v 7, we were asked to write phrases together decimals. Some of the words in the phrase indicate the place-value positions, and also other native in the phrase indicate the digits to it is in used. Currently let"s look at some instances in i m sorry we write these kinds of decimals making use of words.

Example 8: write each decimal using words.

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

Example 9: compose each decimal making use of words.

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

 

Example 10: Write the complying with decimal utilizing 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, 4 hundred five and also eight thousand, three hundred sixty-five millionths

Summary: You learned exactly how to read and also write decimal in this lesson. When writing a blended number together a decimal, the fractional component must be convert to decimal digits. Decimal are called by the place of the last digit. The hyphen is critical indicator when reading and also writing decimals. Once writing a phrase as a decimal, several of the words suggest the place-value positions, and other words suggest the digits to be used.

Exercises

In exercises 1 and also 2, click when in response BOX and kind in her answer; then click ENTER. After you click ENTER, a blog post will show up in the outcomes BOX to show whether her answer is exactly or incorrect. To begin over, click CLEAR.

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price BOX:   

results BOX: 

*
price BOX:   

outcomes BOX: 

In practice 3 through 5, read each inquiry below. Choose your answer by clicking on its button. Feedback to her answer is noted in the outcomes BOX. If you make a mistake, pick a different button.
3.Which that the complying with is same to seven hundred five thousand and also eighty-nine ten-thousandths?
 700.005.089705,000.089705,000.0089705,000.00089

RESULTS BOX: 

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

See more: How Much Does A 500 Gallon Propane Tank Weigh ? Weight Of 500 Gallon Propane Tank

RESULTS BOX: 

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

RESULTS BOX: