Reading Decimal Position on a Number Line: Tenths

In the final lesson, you were introduced to decimal numbers. Decimal places change by a factor of 10. For instance, let'due south look at the number '3247.8956' below.

3	x	1000	thousands
ii	x	100	hundreds
four	x	x	tens
seven	x	1	ones
8	x	0.1	tenths
nine	ten	0.01	hundredths
v	10	0.001	thousandths
6	x	0.0001	ten-thousandths

A decimal number tin can accept a whole-number role and a fractional office.

Mixed Number	- Expanded Class -		Decimal Form
	= (v 10 10) + ( seven 10 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 apply our Identify Value and Decimals Chart (PDF) as a visual reference for the examples presented in this lesson.

Case ane: Write each mixed number as a decimal.

Example 2: Write each phrase as a mixed number and every bit a decimal.

phrase	mixed number	decimal
five and 3 tenths		5.300000
forty-9 and one hundredth		49.010000
two hundred sixteen and two hundred thirty-1 thousandths		216.231000
nine thousand, 10 and three hundred l-9 ten-thousandths		ix,010.035900
seventy-six thousand, fifty-three and forty-vii hundred-thousandths		76,053.000470
two hundred 20-9 thousand and eighty-ane millionths		229,000.000081

Await at the mixed numbers in the examples above. You will discover that the denominator of the partial office is a gene of 10, making it is like shooting fish in a barrel to convert to a decimal. Permit'south look at some examples in which the denominator isnot a cistron of x.

Example three: Write each mixed number as a decimal.

Analysis: A fraction bar tells united states to divide. In society to do this, we must convert or change the partial part of each mixed number to decimal digits. We will do this by dividing the numerator of each fraction by its denominator.

Alternating Method: Information technology should exist noted that some of the fractions higher up could accept been converted to decimals using equivalent fractions. For case:

Instance iv: When asked to writetwo hundred thousandths equally a decimal, iii students gave iii different answers as shown below. Which student had the correct reply?

Educatee 1: 200,000.

Student 2: 0.200

Student iii: 0.00002

Analysis: Let's use our place value chart to help us analyze this problem.

Permit'south look at the expanded class of each decimal to help us detect the correct answer.

Answer: Thus, two hundred thousandths is 0.200, and so Student 2 had the correct answer.

As you tin can meet, decimals are named by the place of the last digit. Observe that in Example 4, the reply given past Student 3 was two hundred-thousandths. This phrase has a hyphen in it. The hyphen is an important slice of information that helps us read and write decimals. Let'due south look at some more examples.

Instance 5: Write each phrase as a decimal.

phrase	assay	fraction	decimal
iii hundred ten thousandths	310 thousandths		0.310
three hundred 10-thousandths	300 ten-thousandths		0.0300

Example vi: Write each phrase as a decimal.

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

Instance 7: Write each phrase every bit a decimal.

phrase	analysis	fraction	decimal
7 hundred millionths	700 millionths		0.000700
seven hundred-millionths	7 hundred-millionths		0.00000007

In Examples 5 through seven, 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 bespeak 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	assay	phrase
0.110	110 thousandths	one hundred 10 thousandths
0.0100	100 10-thousandths	one hundred ten-thousandths

Example 9: Write each decimal using words.

decimal	assay	phrase
0.400	400 thousandths	four hundred thousandths
0.00004	4 hundred-thousandths	four hundred-thousandths

Answer:

The decimalone,729,405.008365 is written as:

one million, seven hundred 20-ix thousand, four hundred five and eight k, three hundred lx-five millionths

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Summary: Y'all learned how to read and write decimals in this lesson. When writing a mixed number as a decimal, the fractional role must exist converted to decimal digits. Decimals are named past 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.

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Exercises

In Exercises one and 2, click once in an ANSWER BOX and type in your answer; and so click ENTER. Later you click ENTER, a message will appear in the RESULTS BOX to point whether your answer is correct or incorrect. To start over, click Articulate.

In Exercises 3 through five, read each question below. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If y'all make a mistake, cull a different button.

3.	Which of the following is equal to 7 hundred five grand and lxxx-nine 10-thousandths?

4.	Which of the post-obit is equal to 9,842.1039?

v.	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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