Read and Write Decimals to the Thousandths

In the final lesson, you lot were introduced to decimal numbers. Decimal places change past a factor of 10. For example, permit's look at the number '3247.8956' below.

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

A decimal number can take a whole-number part and a partial part.

Mixed Number	- Expanded Class -		Decimal Form
	= (5 x 10) + ( vii x 1)	+ (four ten) + (ix 10)	= 57.49
	- whole-number part -	- fractional part -

In this lesson, y'all will learn how to read and write decimals. You lot may use our Identify Value and Decimals Chart (PDF) equally a visual reference for the examples presented in this lesson.

Example 1: Write each mixed number as a decimal.

Example ii: Write each phrase as a mixed number and as a decimal.

phrase	mixed number	decimal
v and iii tenths		5.300000
forty-nine and one hundredth		49.010000
two hundred 16 and two hundred thirty-i thousandths		216.231000
nine thousand, ten and iii hundred fifty-nine 10-thousandths		nine,010.035900
seventy-six yard, fifty-three and forty-seven hundred-thousandths		76,053.000470
two hundred twenty-nine grand and 80-ane millionths		229,000.000081

Look at the mixed numbers in the examples above. You will notice that the denominator of the partial office is a factor of x, making it is like shooting fish in a barrel to convert to a decimal. Let's expect at some examples in which the denominator isnot a gene of 10.

Example three: Write each mixed number as a decimal.

Assay: A fraction bar tells u.s.a. to divide. In society to practise this, we must convert or alter the fractional part of each mixed number to decimal digits. We will do this by dividing the numerator of each fraction by its denominator.

Alternate Method: It should be noted that some of the fractions above could have been converted to decimals using equivalent fractions. For instance:

Example iv: When asked to writetwo hundred thousandths as a decimal, three students gave three dissimilar answers equally shown below. Which pupil had the correct respond?

Student i: 200,000.

Student 2: 0.200

Student 3: 0.00002

Assay: Let's use our place value chart to help the states analyze this problem.

Permit's wait at the expanded grade of each decimal to assistance us observe the right answer.

Respond: Thus, two hundred thousandths is 0.200, so Pupil 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 respond given by Student three was 2 hundred-thousandths. This phrase has a hyphen in it. The hyphen is an important piece of data that helps us read and write decimals. Let's look at some more than 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 half-dozen: Write each phrase equally a decimal.

phrase	analysis	fraction	decimal
eight hundred thousandths	800 thousandths		0.800
eight hundred-thousandths	8 hundred-thousandths		0.00008

Instance vii: 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 seven, nosotros were asked to write phrases equally decimals. Some of the words in the phrase indicate the place-value positions, and other words in the phrase betoken the digits to be used. Now let's look at some examples in which we write these kinds of decimals using words.

Instance 8: Write each decimal using words.

decimal	analysis	phrase
0.110	110 thousandths	one hundred ten thousandths
0.0100	100 ten-thousandths	ane hundred ten-thousandths

Example 9: Write each decimal using words.

decimal	analysis	phrase
0.400	400 thousandths	iv hundred thousandths
0.00004	iv hundred-thousandths	iv hundred-thousandths

Answer:

The decimalane,729,405.008365 is written as:

1 million, seven hundred twenty-ix thousand, four hundred v and eight thousand, three hundred sixty-five millionths

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Summary: Yous 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 identify of the last digit. The hyphen is an of import indicator when reading and writing decimals. When writing a phrase every bit a decimal, some of the words indicate the place-value positions, and other words indicate the digits to be used.

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Exercises

In Exercises 1 and 2, click once in an Respond 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 beneath. Select your answer past clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If yous make a mistake, choose a different push.

3.	Which of the following is equal to seven hundred five yard and eighty-nine x-thousandths?

4.	Which of the following is equal to 9,842.1039?

5.	Which of the following is equal to five hundred-thousandths?

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Source: https://www.mathgoodies.com/lessons/decimals/read_write

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