Which number system decimal numbers use?
Decimal numbers are written using decimal numeral system. Decimal numeral system is
also called as Base Ten Numeral Positional System, which uses 10 as base to write numbers.
This system also uses a decimal point which is represented by a symbol dot ( . ) or comma (
, ).
English speaking countries use dot ( . ) notations to represent decimal numbers. Other countries use comma ( , ) notation for decimal numbers.
Parts of 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 separated 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 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
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.
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.
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
110
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
1100.
Similarly, when the digit moves another place to right its place value becomes
11000
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.
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.
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 1: Convert fraction
13100
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
∴ 13100
can be written in decimal form as 0.13
Example 2: Convert fraction 35710
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
∴ 35710
can be written in decimal form as 35.7
Example 3: Convert fraction 145681000
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
∴ 145681000
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 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 119_____
Step 3: To add the denominator to the above fraction, write digit 1 in the denominator.
1191_____
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 11910
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.
1372_____
Step 3: Write digit 1 in the denominator.
13721_____
There are 2 decimal places in 13.72, so write 2 number of zeros after 1 in the denominator.
so the fraction is 1372100
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.
1189_____
Step 3: Write digit 1 in the denominator.
11891_____
There are 5 decimal places in 0.01189, so write 5 number of zeros after 1 in the denominator.
1189100000
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 1: Convert 4510
into decimals
Here, 4 is a whole number and 510
is a fractional part. whihc is equal to 0.5
∴ 4510
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
510
into decimals, which is 0.5
Step 3: write 0.5 after 4., which becomes 4.5
Example 2: Convert 1284100
into decimals
Step 1: Write the whole number 128 and then decimal after, which is 128.
Step 2: Change the fractional part
4100
into decimals, which is 0.04
Step 3: write 0.04 after 128., which becomes 128.004
Example 1: Convert 1025110
into decimals
Step 1: Write the whole number 1025 and then decimal after, which is 1025.
Step 2: Change the fractional part
110
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 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 + 610
+ 8100
+ 21000
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 + 210
+ 4100
+ 31000
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 + 110 + 2100
- 1 + 21000
- 100 + 10 + 5 + 810
- 90 + 9100
- 6 + 710 + 91000
-
40 + 5 + 110
+ 2100
= 45 + 0.1 + 0.02
= 45.12
-
1 + 21000
= 1 + 0.002
= 1.002
-
100 + 10 + 5 + 810
= 115 + 0.8
= 115.8
-
90 + 9100
= 90 + 0.09
= 90.09
-
6 + 710
+ 91000
= 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 + 1100
-
= 14 + 0.2
= 14 + 210
-
0.69
= 0.6 + 0.09
= 610 + 9100
-
200.008
= 200 + 0.008
= 200 + 81000
-
1.0005
= 1 + 0.0005
= 1 + 510000
5) Turn the following fractions into decimals.
- 147100
- 17510
- 910000
- 7100
- 1432100
- 164841000
-
147100
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
-
17510
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
-
910000
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
-
7100
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 7. So add one extra zero on left of number 7, so the decimal number will become 0.07
-
1432100
1432100 is a mixed fraction which has whole part of 14 and fractional part of 32100.
Step 1: Change the fractional part 32100 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
-
164841000
Step 1: Change the fractional part 4841000 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. 72_____
Step 3: Write digit 1 in the denominator. 721_____
There are 2 decimal places in 0.72, so write 2 number of zeros after 1 in the denominator. 72100
-
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. 89_____
Step 3: Write digit 1 in the denominator. 891_____
There are 1 decimal places in 8.9, so write 1 number of zeros after 1 in the denominator. 8910
-
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. 192_____
Step 3: Write digit 1 in the denominator. 1921_____
There are 3 decimal places in 0.192, so write 3 number of zeros after 1 in the denominator. 1921000
-
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. 14789_____
Step 3: Write digit 1 in the denominator. 147891_____
There are 3 decimal places in 14.789, so write 3 number of zeros after 1 in the denominator. 147891000
-
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. 2019_____
Step 3: Write digit 1 in the denominator. 20191_____
There are 2 decimal places in 20.19, so write 2 number of zeros after 1 in the denominator. 2019100
Write True or False Worksheet
| Type: | True False |
| Count: | 1 |
| S.N. | Statement | ✓ or ✕ |
|---|---|---|
| 1) | 410 = 0.4? | |
| 2) | 8.01 is read as eight and one tenth? | |
| 3) | 7 + 210 + 5100 = 7.25? | |
| 4) | 20 + 5 + 0.1 + 0.01 = 25.011 ? | |
| 5) | 5 + 1100 = 5.01 ? | |
| 6) | The expanded form of 4.007 is 4 + 710000 ? | |
| 7) | The fractional form of 0.008 is 81000 ? | |
| 8) | The decimal form of 9991000 is 9.999? | |
| 9) | The mixed number 2 910 = 2.9? | |
| 10) | 15.37 can be written as 15 + 37100 ? |
Match Columns Worksheets
| Type: | Matching |
| Count: | 2 |
| 1) | Two tenths | a) | 0.009 |
| 2) | Forty five and two tenths | b) | 7.75 |
| 3) | Seven point seven five | c) | 1000.009 |
| 4) | Five and seven hundredths | d) | 7.6 |
| 5) | Nine thousandths | e) | 6.35 |
| 6) | Seven and six tenths | f) | 0.2 |
| 7) | Six and thirty five hundredths | g) | 45.2 |
| 8) | One thousand and nine thousandths | h) | 5.07 |
| 1) | 0.4 | a) | Seventy two thousandths |
| 2) | 0.72 | b) | Four hundredths |
| 3) | 0.072 | c) | One hundredths |
| 4) | 0.04 | d) | Four tenths |
| 5) | 0.07 | e) | Seven hundredths |
| 6) | 0.01 | f) | Seventy two hundredths |
Solve Questions Worksheets
| Type: | Solve Questions |
| Count: | 4 |
Convert fractions into decimals.
| 1) | 1310 | ___________ |
| 2) | 143100 | ___________ |
| 3) | 70981000 | ___________ |
| 4) | 41000 | ___________ |
| 5) | 110000 | ___________ |
| 6) | 165100 | ___________ |
| 7) | 94100 | ___________ |
| 8) | 127510000 | ___________ |
| 9) | 97411000 | ___________ |
| 10) | 181000 | ___________ |
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 | ___________ |
Write the following decimals into words.
- 11.3
- 149.02
- 7.001
- 749.005
- 9.148
Change the following words into numbers.
- Twenty six point one five nine
- Sixty four and two hundredths
- Five and seventy four thousandths
- Sixty five hundredths
- Three tenths
Multiple Choice Questions Worksheet
| Type: | MCQ |
| Count: | 1 |
- 0.1
- 0.01
- 0.001
- 0.100
- 27.5
- 27.05
- 27.50
- 2.75
- 90.78
- 90.87
- 9.078
- 907.8
- ones
- hundredths
- tenths
- thousandths
- 8
- 86
- 25
- 5
- 10.254
- 17.245
- 17.542
- 10.245
- 0.470
- 4.007
- 0.047
- 0.407
- tenths
- hundredths
- thousandths
- tens
- seventy eight and sixty eight hundredths
- seventy eight and sixty eight thousandths
- seventy eight and sixty eight tenths
- seventy eight and sixty eight
- ones
- tens
- tenths
- hundredths
