In the last lesson, friend were introduced to decimal numbers. Decimal places readjust by a variable of 10. Because that example, let\"s look in ~ 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 have the right to have a whole-number part and a spring part.

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

In this lesson, you will certainly learn exactly how to read and write decimals. You might use our Place Value and Decimals Chart (PDF) as a visual referral for the instances presented in this lesson.

Example 1: create each combined number as a decimal.

Mixed NumberDecimal
\"*\"
52.3000
\"*\"
973.4100
\"*\"
31.2670
\"*\"
1842.0056

Example 2: write each expression as a mixed number and also as a decimal.

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

Look at the combined numbers in the instances above. Girlfriend will notification that the denominator of the fractional part is a aspect of 10, making that is easy to convert to a decimal. Let\"s look in ~ some examples in i beg your pardon the denominator is not a factor of 10.

Example 3: Write each combined number as a decimal.

Analysis: A portion bar tells us to divide. In stimulate to perform this, us must convert or change the fractional component of each blended number to decimal digits. We will carry out this by dividing the numerator of each portion by that is denominator.

Mixed NumberFractional PartDecimal
\"*\"
\"*\"
6.9000
\"*\"
\"*\"
9.7200
\"*\"
\"*\"
167.1250
\"*\"
\"*\"
149.5625
\"*\"

Alternate Method: It need to be provided that several of the fractions above could have been convert to decimal using equivalent fractions. Because that example:

\"*\"

Example 4: When asked to write two hundred thousandths as a decimal, 3 students gave three different answers as shown 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 use our ar value graph to help us analysis this problem.

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

Let\"s look at the expanded kind of every decimal to help us find the exactly answer.

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

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

As you can see, decimal are named by the ar of the critical digit. Notice that in instance 4, the answer given by student 3 was 2 hundred-thousandths. This phrase has a hyphen in it. The hyphen is vital piece of information that helps united state read and write decimals. Let\"s look at some more examples.

Example 5: Write each expression as a decimal.

phraseanalysisfractiondecimal
three hundreds ten thousandths 310 thousandths
\"*\"
0.310
three hundred ten-thousandths 300 ten-thousandths
\"*\"
0.0300

Example 6: write each expression as a decimal.

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

Example 7: write each expression as a decimal.

phraseanalysisfractiondecimal
seven hundreds millionths 700 millionths
\"*\"
0.000700
seven hundred-millionths 7 hundred-millionths
\"*\"
0.00000007

In instances 5 with 7, we were request to write phrases as decimals. Several of the native in the phrase indicate the place-value positions, and other words in the phrase suggest the digits to be used. Now let\"s look at some instances in which we compose these kinds of decimals utilizing words.

Example 8: create each decimal making use of words.

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

Example 9: write each decimal using words.

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

 

Example 10: Write the complying with decimal using words. Roll your computer mouse over each digit for help.
  
 
\"*\"

 

Answer: The decimal 1,729,405.008365 is created 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 write decimal in this lesson. Once writing a combined number as a decimal, the fractional part must be convert to decimal digits. Decimals are called by the location of the last digit. The hyphen is critical indicator when reading and writing decimals. When writing a expression as a decimal, few of the words indicate the place-value positions, and other words show the digits to it is in used.

Exercises

In practice 1 and also 2, click as soon as in solution BOX and type in your answer; climate click ENTER. After you click ENTER, a article will appear in the outcomes BOX to suggest whether her answer is correct or incorrect. To start over, click CLEAR.

\"*\"
prize BOX:   

outcomes BOX: 

\"*\"
answer BOX:   

results BOX: 

In exercises 3 through 5, review each question below. Pick your price by clicking its button. Feedback to her answer is provided in the results BOX. If you make a mistake, pick a different button.
3.Which that the following is same to seven hundred 5 thousand and also 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 one thousand, thirty-nine millionthsnine thousand, eight hundred, forty-two and one thousand, thirty-nine ten-thousandthsnine thousand, eight hundred, forty-two and one thousand, thirty-nine thousandthsNone the the above.

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RESULTS BOX: 

5.Which of the following is same to five hundred-thousandths?
 500,0000.5000.00050.00005

RESULTS BOX: