7 Tenths As A Decimal

Introduction

The give-and-take decimal comes from the Latin word "Decem" meaning 10. . In algebra, a decimal number can exist divers every bit a number whose consummate part and the partial part are separated by a decimal betoken. Earlier nosotros learn what we mean past a tenth of decimal it is important to recall the place value system of decimals that defines the position of a tenth in a decimal number.

What are Thousandths in a Decimal?

If an object is divided into 1000 equal parts, then each role is one-thousandth of the whole. This means that –

One thousandth = $\frac{one}{grand}$ which in decimal form is equal to 0.001

If we accept 7 parts out of yard equal parts of an object, then 7 parts make $\frac{vii}{1000}$ of the whole and it is written as 0.007.

Similarly, nosotros have,

$\frac{15}{1000}$ = 0.015

$\frac{131}{m}$ = 0.131

$\frac{974}{yard}$ = 0.974

$\frac{1265}{grand} = \frac{m+265}{1000} = \frac{1000}{k} + \frac{265}{1000} = 1 + 0.265 = one.265$

$\frac{11345}{1000} = \frac{11000+345}{m} = \frac{11000}{grand} + \frac{345}{thousand} = 11 + 0.345 = 11.345$ and so on.

So, how do we obtain the thousandth of a decimal?

The post-obit points need to be considered while writing a thousandth of a decimal number –

A fraction of the form $\frac{Number}{yard}$ is written as a decimal obtained by putting decimal point by leaving iii right most digits.
If the number is short of digits, nosotros insert zeros at the left of the number.

Now, permit united states of america acquire well-nigh the placement of the thousandths of a decimal in the Place Value System. But before that, we must recall what we mean by the place value system of decimals.

Place Value System of Decimals

Nosotros know that each place in the identify value table has a value x times the value of the adjacent identify on its right. In other words, the value of a place is one-tenth of the value of the next place on its left. We detect that if one digit moves i place left to correct its value becomes one-tenth ($\frac{1}{10}$ ) of its previous value and when information technology moves two places left to correct its value comes ane-hundredth ( $\frac{i}{100}$ ) of its previous term and so on. Therefore, if nosotros wish to movement beyond ones place which is the instance of decimals, we will have to extend the place value table by introducing the places of tenths ($\frac{ane}{ten}$ ), hundredths ($\frac{1}{100}$ ), thousandths ( $\frac{one}{1000}$ ) and so on.

Therefore, the identify value table in case of a decimal number volition be of the form –

Thousands ( yard )	Hundreds ( 100 )	Tens (10)	Ones ( ane )	Tenths ($\frac{1}{10}$)	Hundredths ( $\frac{ane}{100}$ )	Thousandths ( $\frac{1}{1000}$ )

For instance, the decimal number 257.32 in the place value arrangement will be written as –

Hundreds	Tens	Ones	Tenths	Hundredths
two	v	seven	3	2

A decimal or a decimal number may contain a whole number part and a decimal part. The following table shows the whole number role and the decimal part of some decimals –

Number	Whole Number Part	Decimal Part
xiii.95	xiii	95
9.053	nine	053
0.148	0	148
65.0	65	0
17	17	0
0.003	0	003
0.2	0	2

Now, how do we read the decimals using the place value system? Let us observe out.

Reading the Decimal Numbers using the Place Value System

In order to read decimals, the post-obit steps are used –

Read the whole number office
Read the decimal indicate as point
Read the number to the right of the decimal signal. For example, 14.35 will be read every bit Fourteen point three five. Alternatively, the number to the right of the decimal betoken can besides be read past reading the number to the right of the decimal indicate and naming the place value of the last digit. For instance, the number 8.527 can too be read every bit 8 and five hundred twenty 7 thousandths.

Now let us run across how to read and write the thousandths of a decimal in the Place Value Arrangement.

Thousandths of a decimal in the Identify Value System

From the place value table above, we tin run across that the thousandth of a decimal is placed at the third digit to the correct of the decimal point. Therefore, this is the position of the thousandth in the identify value system. Let us understand the thousandth position of some numbers every bit an case.

Suppose we have the following numbers and we want to identify the digit at the thousandth place in these numbers.

12.6587
0.02369
1.001127

Allow usa check these numbers one by 1.

We have the number 12.6587. Bank check the digit at the third position from the right of the decimal. The number is viii. This is the thousandth place of the number having the identify value 0.008.
Adjacent, we have the number 0.02369. Check the digit at the third position from the correct of the decimal. The number is 3. This is the thousandth place of the number having the place value 0.003.
Now, we take the number ane.00127. Bank check the digit at the 3rd position from the right of the decimal. The number is one. This is the thousandth identify of the number having the place value 0.001.

Now, let us understand the representation of the thousandth of a decimal on a number line.

Representation of Thousandths of a decimal on a Number Line

Before nosotros learn how to represent a 10th on a number permit us recall what nosotros sympathize by the term number line.

What is a number line?

A number line is a straight horizontal line with numbers placed at even intervals that provides a visual representation of numbers. Primary operations such as improver, subtraction, multiplication, and division can all be performed on a number line. The numbers increase as we motion towards the right side of a number line while they decrease as we movement left.

Representation of a Thousandth on a Number Line

Higher up is a visual representation of a standard number line. As is clearly visible, as we motion from left to right, there is an increase in the value of numbers while it decreases when we motility from right to left.

We already know how to stand for fractions on a number line. Let u.s. now correspond the thousandths of a decimal on a number line. We can empathise this by an example.

To represent vii.iv on a number line, we first depict 10 lines dividing the total distance betwixt 7 and 8 into 10 equal parts.

We can see that the pointer is iv parts to the correct of the whole number 7.

Similarly, to represent 7.45 on a number line, we first draw 10 lines dividing the full altitude betwixt 7.four and 7.5 into x equal parts.

We can see that the arrow is five parts to the right of the decimal number 7.40.

Next, to correspond 7.456 on a number line, nosotros kickoff draw 10 lines dividing the full distance between 7.45 and 7.46 into x equal parts.

We tin can see that the arrow is six parts to the right of the decimal number 7.45

So, in this manner, we have represented the number 7.456 on the number line.

The steps that we used above to represent a 10th on a number line tin can be summarised equally –

Nosotros draw a number line between 0 and 1.
We then depict 10 lines dividing the total altitude between 0 and 1 into 10 equal parts.
At present, one whole divided into 10 parts is equal to $\frac{1}{10}$.
$\frac{1}{10}$ in decimal form is equal to 0.ane.
At each new line, we are adding $\frac{1}{10}$ or 0.1.
Then, betwixt 0 and 1 nosotros accept, 0 . 1 , 0 . ii , . 0 . three , 0 . 4 , 0 . 5 , 0 . 6 , 0 . seven , 0 . 8 and 0 . nine. Similarly, between 1 and 2 we have, 1 . one , one . 2 , 1 . 3 , 1 . iv , ane . 5 , one . half dozen , 1 . vii , one . 8 and 1 . 9.
We can also say that the line representing $\frac{1}{two}$ or 0.5 is the half way mark between 0 and 1. Similarly, the line representing $i\frac{5}{10}$ or 1.5 is the half fashion mark between 1 and 2.
Ten tenths is equal to ane whole.
Side by side, we perform the same steps to draw ten lines dividing the total distance betwixt 0.01 and 0.02 into x equal parts.
Again, we perform the same steps to draw ten lines dividing the full altitude between 0.001 and 0.002 into ten equal parts.
In this manner, we can plot the thousandth of a decimal on a number line.

The above process can exist defined equally – "To correspond a thousandth on a number line, nosotros will first have to divide the altitude between two whole numbers into 10 equal parts to get their tenths values. Next, we split once again the distance between 2 tenths to get their hundredths values. Finally, we divide the distance between two hundredths into 10 equal parts to get their thousandths values."

At present let us go through some solved examples on the thousandth of a decimal.

Solved Examples

Example 1 Write each of the following decimals in words

viii.005
0.635
250.005
0.705

Solution We have been given four decimal numbers and we need to write them in words. Permit u.s. do them one past one.

8.005

Nosotros tin can see that the given decimal number has three digits on the right of the decimal point. Therefore, nosotros will take to read the given decimal number until its thousandth part.

The number in words will exist written as –

"Eight betoken zero cipher five". Some other way to read the given decimal number is

"8 and Five Thousandth"

Therefore, viii.005 in words will be "Eight point nada zero 5" or "Eight and Five Thousandth"

0.635

We tin meet that the given decimal number has 3 digits on the right of the decimal betoken. Therefore, we will have to read the given decimal number until its thousandth part.

The number in words will exist written as –

"Nothing point six three five". Some other fashion to read the given decimal number is

"Zero and Vi Hundred and xxx 5 thousandth"

Therefore, 0.635 in words will be "Nada bespeak six three v" or "Zero and Six Hundred and thirty five thousandth"

250.005

We can see that the given decimal number has three digits on the right of the decimal point. Therefore, we volition have to read the given decimal number until its thousandth part.

The number in words will be written as –

"Two hundred and fifty betoken null nothing five". Another manner to read the given decimal number is

"Ii hundred and 50 and five thousandth"

Therefore, 250.005 in words will exist "Two hundred and fifty point zero cipher five" or "Ii hundred and fifty and five thousandth".

0.705

We can see that the given decimal number has 3 digits on the right of the decimal point. Therefore, we volition have to read the given decimal number until its thousandth function.

The number in words volition exist written as –

"Zero point seven zip five". Another way to read the given decimal number is

"Zilch and seven hundred and five thousandth"

Therefore, 250.005 in words volition exist "Zip bespeak seven zero five" or "Nix and seven hundred and five thousandth".

Case two Write each of the following as a decimal number

$7 + \frac{2}{10} + \frac{8}{100} + \frac{6}{1000}$
$\frac{3}{100} + \frac{7}{yard}$
$\frac{2}{10} + \frac{3}{100} + \frac{7}{m}$

Solution We take been given 3 values in the fractional grade and nosotros need to write their equivalent decimal class. Allow united states of america exercise them i by one.

$7 + \frac{2}{10} + \frac{8}{100} + \frac{6}{chiliad}$

Nosotros tin see that the given fraction has one whole number and three fractional parts. Each one of the given partial values will be needed to be converted into the corresponding decimal value to get the desired number. So, nosotros accept.

7 is a whole number and so we demand not change into any other form.

We know that $\frac{2}{10}$ = 0.two and is chosen ii tenths or ii tenths.

Similarly, $\frac{viii}{100}$ = 0.08 and is called viii hundredths or 8 hundredths

Likewise, $\frac{6}{yard}$ = 0.006 and is called six thousandths or 6 thousandths

Therefore, the give fraction in the decimal form will be

$7 + \frac{2}{10} + \frac{8}{100} + \frac{6}{1000}$ = seven + 0.ii + 0.08 + 0.006 = seven.286

$\frac{3}{100} + \frac{seven}{1000}$

Nosotros can see that the given fraction has no whole number and two fractional parts. Also, it is important to see that that there is no value corresponding to one-tenth of a decimal. Each one of the given fractional values volition exist needed to be converted into the corresponding decimal value to get the desired number. So, we take.

Nosotros volition place a 0 for a whole number as there is no whole number value in the given fraction.

Similarly, we will place a 0 for the 10th of a decimal number equally at that place is no value respective to one-10th of a decimal.

Now, $\frac{3}{100}$ = 0.03 and is called 3 hundredths or three hundredths

Also, $\frac{7}{yard}$ = 0.007 and is called seven thousandths or seven thousandths

Therefore, the given fraction in the decimal form volition be

$\frac{iii}{100}$ + $\frac{7}{1000}$ = 0 + 0.0 + 0.03 + 0.007 = 0.037

$\frac{2}{10}$ + $\frac{3}{100}$ + $\frac{7}{k}$

We tin see that the given fraction has no whole number and ii fractional parts. Each one of the given fractional values will be needed to be converted into the corresponding decimal value to get the desired number. So, we take.

We will identify a 0 for a whole number every bit there is no whole number value in the given fraction.

We know that $\frac{2}{10}$ = 0.2 and is called two tenths or ii tenths.

At present, $\frac{3}{100}$ = 0.03 and is chosen three hundredths or three hundredths

Besides, $\frac{seven}{1000}$ = 0.007 and is called 7 thousandths or 7 thousandths

Therefore, the given fraction in the decimal form will be

$\frac{2}{10}$ + $\frac{three}{100}$ + $\frac{7}{1000}$ = 0.2 + 0.03 + 0.007 = 0.237

Key Facts and Summary

A decimal number can be defined equally a number whose complete part and the fractional part are separated by a decimal point.
The Identify Value Arrangement is the organization in which theposition of a digit in a number determines its value. The identify value of a digit in a number is the value it holds to be at the identify in the number.
In gild to read decimals, we offset
Read the whole number part
Read the decimal point as a signal.
If an object is divided into 1000 equal parts each function is 1 thousandth of the whole.
I thousandth = $\frac{1}{m}$ which in decimal grade is equal to 0.001
A number line is a directly horizontal line with numbers placed at even intervals that provides a visual representation of numbers. Chief operations such as addition, subtraction, multiplication, and division tin can all be performed on a number line.
To represent a thousandth on a number line, we will get-go have to separate the distance between two whole numbers into 10 equal parts to get their tenth values. Next, we divide again the distance between 2 tenths to get their hundredths values. Finally, we divide the altitude between two hundredths into 10 equal parts to get their thousandths values.

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