Chapter Contents

Basics
Parts of a decimal number
Place value chart of decimal numbers
How to read decimal numbers?
Writing fractions into decimals
Writing decimals into fractions
Writing mixed fractions into decimals
Expanding decimal numbers
Examples
Worksheet 1
Worksheet 2
Worksheet 3
Worksheet 4
Worksheet 5
Worksheet 6
Worksheet 7
Worksheet 8

Decimal Numbers, Converting Decimals to Fractions

Chapter Contents

Basics
Parts of a decimal number
Place value chart of decimal numbers
How to read decimal numbers?
Writing fractions into decimals
Writing decimals into fractions
Writing mixed fractions into decimals
Expanding decimal numbers
Examples
Worksheet 1
Worksheet 2
Worksheet 3
Worksheet 4
Worksheet 5
Worksheet 6
Worksheet 7
Worksheet 8

Basics

Decimal numeral system is a system for writing integer and non integer numbers. Decimal numeral system is also called as Base Ten Numeral Positional System. It means that this system uses 10 as base.
So, decimal refers to notation of a number in decimal numeral system. The symbol used for its notation is a dot ( . ) or comma ( , ).

Note

English speaking countries use dot ( . ) notations to represent decimal numbers. Other countries use comma ( , ) notation for decimal numbers.

Parts of a decimal number

A decimal number always has two parts, one is whole number part and the another part is decimal part. Both parts are always seperated by dot ( . ) or comma ( , ).

The part of the number which is written before the decimal is called as whole part and the part written after the decimal is called as the decimal part.

Example

Example 1: Write the whole part and decimal part of decimal number 1.3
Here, 1 is the whole number part.
3 is the decimal part.

Example 2: Write the whole part and decimal part of decimal number 23.14
Here, the number 23 which is written before the decimal is the whole number part.
The number 41 which is written after the decimal is the decimal part.

Place value chart of decimal numbers

The figure below is the place value chart which is used to find the value of a digit in a decimal number at a place. This chart also helps in how to read a decimal number and how to write an expanded form of a decimal number.

Place value chart

In the place value chart there are boxes on left and right sides of the decimal box. Each box on left and right side of the decimal box represent a place of a digit. Let’s understand with an example how to a decimal number is represented in using place value chart.

In the above chart, each place is ten times the value of next place value on its right. It means place value of a digit increases by 10 times when it moves by one place from right to left.
The value of ten’s place is 10 times the ones place. The value of hundreds place increases by 10 times of tens place.

Example

Representation of 683.125 on place value chart
683.125 can be represented using the following place value chart.
The digits 683 which are present on left side of the decimal number 683.125 are shown in the chart in the boxes which are present on the same left side of the decimal box.
The digits 125 which are present on right side of the decimal number 683.125 are shown in the boxes which are on the right side of the decimal box.

So, when moving one place to the right inits digit, the place value of a digit decreases. Place value of the digit will be $\frac{1}{10}$ or one tenth. So, here, tenths means one whole is divided into ten equal parts and each part is called one tenth.
Again, when the digit moves one more place right of tenth, place value of the digit will be $\frac{1}{100}$ .
Similarly, when the digit moves another place to right its place value becomes $\frac{1}{1000}$ or one thousandths.

How to read decimal numbers?

The decimal numbers can be read in two different ways.

1. The whole part of a decimal number is read as we read out a number in general but the digits present in decimal part is read out with their place name of digits.

Example

2.7
2.7 is read as two and seven tenths.

14.25
14.25 is read as fourteen and twenty five hundredths.

4.725
4.725 is read as four and seven hundred and twenty five hundredths.

2. The whole part of a decimal number is read as we read out a number in general, then read out decimal as point and lastly read out each digit present in decimal part separately.

Example

2.7
2.7 is read as two point seven.

14.25
14.25 is read as fourteen point two five.

4.725
4.725 is read as four point seven hundred two five.

Writing fractions into decimals

Fractions with denominators 10, 100, 1000 etc. can be written into decimal numbers. So what are the steps to convert fractions into decimals?
Step 1: Count the number of zeros in the denominator.
Step 2: Write the value of the numerator.
Step 3: Move from right to left of the numerator. Count the number of digits when moving from right to left direction. Number of digits moved must be equal to the number of zeros in denominator. After moving put point ‘.‘ on the left of the last number reached.
Step 4: In case if there are no more digits left on the left of ‘.‘, put an additional zero on the left of the ‘.‘.

Example

Example 1: Convert fraction $\frac{13}{100}$ into decimals
Step 1: Count the number of zeros in the denominator 100, which are 2.
Step 2: Write the value of the numerator which is 13.
Step 3: Move from right to left of the numerator 13 by 2 digits, where 2 is the number of zeros in the denominator. Put point after moving 2 digits. So the number becomes .13
Step 4: As .13 has more digits left on the left of ‘.‘, so put an additional zero on the left of the ‘.‘. So the number becomes 0.13
∴ $\frac{13}{100}$ can be written in decimal form as 0.13

Example 2: Convert fraction $\frac{357}{10}$ into decimals
Step 1: The number of zeros in the denominator 10 is 1.
Step 2: Write the value of the numerator which is 357.
Step 3: Move from right to left of the numerator 357 by 1 digit, where 1 is the number of zeros in the denominator. Put point after moving 1 digit. So the number becomes 35.7
∴ $\frac{357}{10}$ can be written in decimal form as 35.7

Example 3: Convert fraction $\frac{14568}{1000}$ into decimals
Step 1: The number of zeros in the denominator 1000 are 3.
Step 2: Write the value of the numerator which is 14568.
Step 3: Move from right to left of the numerator 14568 by 3 digits, where 3 is the number of zeros in the denominator. Put point after moving 3 digits. So the number becomes 14.568
∴ $\frac{14568}{1000}$ can be written in decimal form as 14.568

Writing decimals into fractions

Fractions can also be written into decimals. Let’s take a look at the steps, how to convert decimals into fractions.
Step 1: Count the number of decimal places.
Step 2: Remove the decimal point and the digits after the decimal. After removing write the number obtained as the numerator of the fraction.
Step 3: To add the denominator to the above fraction, write digit 1 in the denominator and then write number of zeros after 1 equal to the number of decimal places present in the given decimal number.

Example

Example 1: Convert decimal 11.9 into fractions
Step 1: Count the number of decimal places in 11.9, which is 1.
Step 2: Remove the decimal point. After removing the number becomes 119 and write this number as the numerator of the fraction.
∴ the fraction becomes $\frac{119}{_____}$
Step 3: To add the denominator to the above fraction, write digit 1 in the denominator. $\frac{119}{1_____}$
Then write number of zeros after 1 equal to the number of decimal places present in 11.9, which is 1.
So, finally the fraction becomes $\frac{119}{10}$

Example 2: Convert decimal 13.72 into fractions
Step 1: Count the number of decimal places in 13.72, which are 2.
Step 2: After removing the decimal point, number becomes 1372.
Write 1372 in the numerator. $\frac{1372}{_____}$
Step 3: Write digit 1 in the denominator. $\frac{1372}{1_____}$
There are 2 decimal places in 13.72, so write 2 number of zeros after 1 in the denominator.
so the fraction is $\frac{1372}{100}$

Example 3: Convert decimal 0.01189 into fractions
Step 1: Count the number of decimal places in 0.01189, which are 5.
Step 2: After removing the decimal point, number becomes 01189 or it can be written as 1189 after omitting the zero at the start.
Write 1189 in the numerator. $\frac{1189}{_____}$
Step 3: Write digit 1 in the denominator. $\frac{1189}{1_____}$
There are 5 decimal places in 0.01189, so write 5 number of zeros after 1 in the denominator. $\frac{1189}{100000}$

Writing mixed fractions into decimals

Mixed fractions can be converted into decimals also. The very first step is to write the whole number of the mixed fraction and put the decimal point after. Then change the fractional part into decimal and write after the whole part with decimal. Let’s look at the solved examples to know it better.

Example

Example 1: Convert $4 \frac{5}{10}$ into decimals
Here, 4 is a whole number and $\frac{5}{10}$ is a fractional part. whihc is equal to 0.5
∴ $4 \frac{5}{10}$ is written as 4.5
Step 1: Write the whole number 4 and then decimal after, which is 4.
Step 2: Change the fractional part $\frac{5}{10}$ into decimals, which is 0.5
Step 3: write 0.5 after 4., which becomes 4.5

Example 2: Convert $128 \frac{4}{100}$ into decimals
Step 1: Write the whole number 128 and then decimal after, which is 128.
Step 2: Change the fractional part $\frac{4}{100}$ into decimals, which is 0.04
Step 3: write 0.04 after 128., which becomes 128.004

Example 1: Convert $1025 \frac{1}{10}$ into decimals
Step 1: Write the whole number 1025 and then decimal after, which is 1025.
Step 2: Change the fractional part $\frac{1}{10}$ into decimals, which is 0.1
Step 3: write 0.1 after 1025., which becomes 1025.01

Expanding decimal numbers

Expanding form of a decimal number helps to understand the value of each digit in the number. It can be written in words as well as in numbers. Let’s learn by example how to expand the decimal numbers.

Example

Example 1: Expand 45.682
45.682 can be represented as following in a place value chart of decimal numbers.

The above chart shows the place value of 4 at tens, 5 at ones, 6 at tenths, 8 at hundredths and 2 at thousandths.
So, its expandable form in words can be written as 4 tens + 5 ones + 6 tenths + 8 hundredths + 2 thousandths
Its expandable form in numbers with fractions will be 40 + 5 + $\frac{6}{10}$ + $\frac{8}{100}$ + $\frac{2}{1000}$
Or, in decimal expansion, it can be written as 40 + 5 + 0.6 + 0.08 + 0.002

Example 2: Expand 785.243
Place value of chart of 785.243 is: numbers.

The above chart shows the place value of 7 at hundreds, 8 at tens, 5 at ones,2 at tenths, 4 at hundredths and 3 at thousandths.
So, its expandable form in words is 7 hundreds + 8 tens + 5 ones + 2 tenths + 4 hundredths + 3 thousandths
Its expandable form in numbers with fractions is 700 + 80 + 5 + $\frac{2}{10}$ + $\frac{4}{100}$ + $\frac{3}{1000}$
In decimal expansion, it can be written as 700 + 80 + 5 + 0.2 + 0.04 + 0.003

Solved Examples

1) Write the following decimals into words.

18.23
0.5
108.743
76.003
5.01

18.23
Eighteen point two three
or
Eighteen and twenty three hundredths
0.5
Zero point five
or
Five tenths
108.743
One hundred eight point seven four three
or
One hundred eight and seven hundred forty three thousandths
76.003
Seventy six point zero zero three
or
Seventy six and three thousandths
5.01
Five point zero one
or
Five and one hundredths

2) Write the following numbers in words to decimal numbers.

Four and fourteen hundredth
One hundred forty nine point zero seven
Sixty nine and two thousandths
Zero point seven two
Fourteen hundredths

Four and fourteen hundredth
4.14
One hundred forty nine point zero seven
149.07
Sixty nine and two thousandths
69.002
Zero point seven two
0.72
Fourteen hundredths
0.14

3) Write the decimal for following expansions.

40 + 5 + $\frac{1}{10}$ + $\frac{2}{100}$
1 + $\frac{2}{1000}$
100 + 10 + 5 + $\frac{8}{10}$
90 + $\frac{9}{100}$
6 + $\frac{7}{10}$ + $\frac{9}{1000}$

40 + 5 + $\frac{1}{10}$ + $\frac{2}{100}$
= 45 + 0.1 + 0.002
= 45.12
1 + $\frac{2}{1000}$
= 1 + 0.002
= 1.002
100 + 10 + 5 + $\frac{8}{10}$
= 115 + 0.8
= 115.8
90 + $\frac{9}{100}$
= 90 + 0.09
= 90.09
6 + $\frac{7}{10}$ + $\frac{9}{1000}$
= 6 + 0.7 + 0.009
= 6.709

4) Change the following decimal numbers into expansion form.

3.01
14.2
0.69
200.008
1.0005

3.01
= 3 + 0.01
= 3 + $\frac{1}{100}$
= 14 + 0.2
= 14 + $\frac{2}{10}$
0.69
= 0.6 + 0.09
= $\frac{6}{10}$ + $\frac{9}{100}$
200.008
= 200 + 0.008
= 200 + $\frac{8}{1000}$
1.0005
= 1 + 0.0005
= 1 + $\frac{5}{10000}$

5) Turn the following fractions into decimals.

$\frac{147}{100}$
$\frac{175}{10}$
$\frac{9}{10000}$
$\frac{7}{100}$
$14 \frac{32}{100}$
$16 \frac{484}{1000}$

$\frac{147}{100}$
To change a fraction into decimal, follow the steps as below:
Step 1: Write the numerator, which is 147
Step 2: As there are two zeros in the denominator. So, put the symbol point after leaving two digits from right to left. The two positions from right to left are 47 in 147. So the decimal number will become 1.47
$\frac{175}{10}$
Step 1: Write the numerator 175
Step 2: As there is one zero in the denominator. So, put the symbol point after leaving one digit from right to left. So the decimal number will become 17.5
$\frac{9}{10000}$
Step 1: Write the numerator 9
Step 2: As there are four zeros in the denominator. So, put the symbol point after leaving four digits from right to left. But there is only one digit in number 9. So add three extra zeros on left of number 9, so the decimal number will become 0.0009
$\frac{7}{100}$
Step 1: Write the numerator 7
Step 2: As there are two zeros in the denominator. So, put the symbol point after leaving two digits from right to left. But there is only one digit in number 8. So add one extra zero on left of number 7, so the decimal number will become 0.07
$14 \frac{32}{100}$
$14 \frac{32}{100}$ is a mixed fraction which has whole part of 14 and fractional part of $\frac{32}{100}$ .
Step 1: Change the fractional part $\frac{32}{100}$ into decimal.
As there are two zeros in the denominator. So, put the symbol point after leaving two digits from right to left. So the decimal number will become 0.32
Step 2: Write the whole part 14
Step 3: Put the symbol point after whole part 14. Write the decimal number 0.32, obtained in step 1, after the decimal. Finally the decimal number becomes 14.32
$16 \frac{484}{1000}$
$\frac{484}{1000}$ .
Step 1: Change the fractional part $\frac{484}{1000}$ into decimal.
As there are three zeros in the denominator. So, put the symbol point after leaving three digits from right to left. So the decimal number will become 0.484
Step 2: Write the whole part 16
Step 3: Put the symbol point after whole part 16. Write the decimal number 0.484, obtained in step 1, after the decimal. Finally the decimal number becomes 16.484

6) Write the following decimals into fractions.

0.72
8.9
0.192
14.789
20.19

0.72
Step 1: Count the number of decimal places in 0.72, which are 2.
Step 2: After removing the decimal point, number becomes 072 or it can be written as 72 after omitting the zero at the start.
Write 72 in the numerator. $\frac{72}{_____}$
Step 3: Write digit 1 in the denominator. $\frac{72}{1_____}$
There are 2 decimal places in 0.72, so write 2 number of zeros after 1 in the denominator. $\frac{72}{100}$
8.9
Step 1: Count the number of decimal places in 8.9, which is 1.
Step 2: After removing the decimal point, number becomes 89.
Write 89 in the numerator. $\frac{89}{_____}$
Step 3: Write digit 1 in the denominator. $\frac{89}{1_____}$
There are 1 decimal places in 8.9, so write 1 number of zeros after 1 in the denominator. $\frac{89}{10}$
0.192
Step 1: Count the number of decimal places in 0.192, which is 3.
Step 2: After removing the decimal point, number becomes 192.
Write 192 in the numerator. $\frac{192}{_____}$
Step 3: Write digit 1 in the denominator. $\frac{192}{1_____}$
There are 3 decimal places in 0.192, so write 3 number of zeros after 1 in the denominator. $\frac{192}{1000}$
14.789
Step 1: Count the number of decimal places in 14.789, which is 3.
Step 2: After removing the decimal point, number becomes 14789.
Write 14789 in the numerator. $\frac{14789}{_____}$
Step 3: Write digit 1 in the denominator. $\frac{192}{1_____}$
There are 3 decimal places in 14.789, so write 3 number of zeros after 1 in the denominator. $\frac{14789}{1000}$
20.19
Step 1: Count the number of decimal places in 20.19, which is 2.
Step 2: After removing the decimal point, number becomes 2019.
Write 2019 in the numerator. $\frac{2019}{_____}$
Step 3: Write digit 1 in the denominator. $\frac{2019}{1_____}$
There are 2 decimal places in 20.19, so write 2 number of zeros after 1 in the denominator. $\frac{2019}{100}$

Worksheet 1

Convert fractions into decimals.

1)	$\frac{13}{10}$	___________
2)	$\frac{143}{100}$	___________
3)	$\frac{7098}{1000}$	___________
4)	$\frac{4}{1000}$	___________
5)	$\frac{1}{10000}$	___________
6)	$\frac{165}{100}$	___________
7)	$\frac{94}{100}$	___________
8)	$\frac{1275}{10000}$	___________
9)	$\frac{9741}{1000}$	___________
10)	$\frac{18}{1000}$	___________

Worksheet 2

Convert decimals into fractions.

1)	0.7	___________
2)	14.89	___________
3)	0.005	___________
4)	1.02	___________
5)	114.1	___________
6)	94.27	___________
7)	4.005	___________
8)	1.007	___________
9)	9.275	___________
10)	994.007	___________

Worksheet 3

Write True or False in the boxes.

1)	$\frac{4}{10} = 0.4$ ?	▭
2)	8.01 is read as eight and one tenth?	▭
3)	$7 + \frac{2}{10} + \frac{5}{100} = 7.25$ ?	▭
4)	$20 + 5 + 0.1 + 0.01 = 25.011$ ?	▭
5)	$5 + \frac{1}{100} = 5.01$ ?	▭
6)	4.007 can be written in expanded form as $4 + \frac{7}{10000}$ ?	▭
7)	The fractional form of 0.008 is $\frac{8}{1000}$ ?	▭
8)	The decimal form of $\frac{999}{1000}$ is 9.999?	▭
9)	The mixed number $2 \frac{9}{10} = 2.9$ ?	▭
10)	15.37 can be written as $15 + \frac{37}{100}$ ?	▭

Worksheet 4

Match the following.

1)	Two tenths	a)	0.009
2)	Forty five and two tenths	b)	7.75
3)	Seven point seven five	a)	1000.009
4)	Five and seven hundredths	c)	7.6
5)	Nine thousandths	d)	6.35
6)	Seven and six tenths	e)	0.2
7)	Six and thirty five hundredths	f)	45.2
8)	One thousand and nine thousandths	g)	5.07

Worksheet 5

Match the following.

1)	0.4	a)	Seventy two thousandths
2)	0.72	b)	Four hundredths
3)	0.072	a)	one tenths
4)	0.04	c)	four tenths
5)	0.07	d)	seven thousandths
6)	0.01	e)	Seventy two hundredths

Worksheet 6

Write the following decimals into words.

1) 11.3

2) 149.02

3) 7.001

4) 749.005

5) 9.148

Worksheet 7

Change the following words into numbers.

1) Twenty six point one five nine

2) Sixty four and two hundredths

3) Five and seventy four thousandths

4) Sixty five hundredths

5) Three tenths

Worksheet 8

Multiple choice questions

1) The number $\frac{1}{100}$ can be written in decimal form as

0.1
0.01
0.001
0.100

2) 20 + 7 + 0.05 =

27.5
27.05
27.50
2.75

3) Ninety point seven eight is written in the number form as

90.78
90.87
9.078
907.8

4) The place value of digit 8 in number 125.008 is

ones
hundredths
tenths
thousandths

5) The fractional part in number 86.25 is

6) The correct value of 10 + 7 + $\frac{2}{10}$ + $\frac{4}{100}$ + $\frac{5}{1000}$ is

10.254
17.245
17.542
10.245

7) The correct decimal value of $\frac{4}{10}$ + $\frac{7}{1000}$ will be

0.470
4.007
0.047
0.407

8) The place value of digit 5 in number 40 + 7 + 0.2 + 0.005 is

tenths
hundredths
thousandths
tens

9) 78.68 is written in word as

seventy eight and sixty eight hundredths
seventy eight and sixty eight thousandths
seventy eight and sixty eight tenths
seventy eight and sixty eight

10) The place value of digit 5 in the number 5.00 is

ones
tens
tenths
hundredths

MCQ Answer Key Hide Show

Last updated on: 28-09-2024

Related chapters

Fractions & Types of Fractions and Applications

Percentages, Convert it to Fractions & Decimals

Digit, Face, Place Values and Comparison of Numbers

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Decimal Numbers, Converting Decimals to Fractions

Basics

Parts of a decimal number

Place value chart of decimal numbers

How to read decimal numbers?

Writing fractions into decimals

Writing decimals into fractions

Writing mixed fractions into decimals

Expanding decimal numbers

Solved Examples

1) Write the following decimals into words.

2) Write the following numbers in words to decimal numbers.

3) Write the decimal for following expansions.

4) Change the following decimal numbers into expansion form.

5) Turn the following fractions into decimals.

6) Write the following decimals into fractions.

Worksheet 1

Convert fractions into decimals.

Worksheet 2

Convert decimals into fractions.

Worksheet 3

Write True or False in the boxes.

4 10 = 0.4 ?

8.01 is read as eight and one tenth?

7 + 2 10 + 5 100 = 7.25 ?

20 + 5 + 0.1 + 0.01 = 25.011 ?

5 + 1 100 = 5.01 ?

4.007 can be written in expanded form as 4 + 7 10000 ?

The fractional form of 0.008 is 8 1000 ?

The decimal form of 999 1000 is 9.999?

The mixed number 2 9 10 = 2.9 ?

15.37 can be written as 15 + 37 100 ?

Worksheet 4

Match the following.

Worksheet 5

Match the following.

Worksheet 6

Write the following decimals into words.

1) 11.3

2) 149.02

3) 7.001

4) 749.005

5) 9.148

Worksheet 7

Change the following words into numbers.

1) Twenty six point one five nine

2) Sixty four and two hundredths

3) Five and seventy four thousandths

4) Sixty five hundredths

5) Three tenths

Worksheet 8

Multiple choice questions

1) The number 1 100 can be written in decimal form as

2) 20 + 7 + 0.05 =

3) Ninety point seven eight is written in the number form as

4) The place value of digit 8 in number 125.008 is

5) The fractional part in number 86.25 is

6) The correct value of 10 + 7 + 2 10 + 4 100 + 5 1000 is

7) The correct decimal value of 4 10 + 7 1000 will be

8) The place value of digit 5 in number 40 + 7 + 0.2 + 0.005 is

9) 78.68 is written in word as

10) The place value of digit 5 in the number 5.00 is

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$\frac{4}{10} = 0.4$ ?

$7 + \frac{2}{10} + \frac{5}{100} = 7.25$ ?

$20 + 5 + 0.1 + 0.01 = 25.011$ ?

$5 + \frac{1}{100} = 5.01$ ?

4.007 can be written in expanded form as $4 + \frac{7}{10000}$ ?

The fractional form of 0.008 is $\frac{8}{1000}$ ?

The decimal form of $\frac{999}{1000}$ is 9.999?

The mixed number $2 \frac{9}{10} = 2.9$ ?

15.37 can be written as $15 + \frac{37}{100}$ ?

1) The number $\frac{1}{100}$ can be written in decimal form as

6) The correct value of 10 + 7 + $\frac{2}{10}$ + $\frac{4}{100}$ + $\frac{5}{1000}$ is

7) The correct decimal value of $\frac{4}{10}$ + $\frac{7}{1000}$ will be