Decimal Numeral System & How To Convert To Fractions

Decimal numeral system

Decimal numbers are written using the decimal numeral system. The Decimal numeral system is also called the 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 the whole number part and the other part is the 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 the whole part and the part written after the decimal is called the decimal part.

Examples of parts of decimal number

Write the whole part and decimal part of decimal number 1.3

Here, 1 is the whole number part.

3 is the decimal part.

Shade one box and 3 boxes out of 10 for whole and decimal parts of 1.3

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.

Place value chart

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

In the above chart, each place is ten times the value of the next place value on its right. It means the 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.

Examples of place value chart

Representation of 683.125 on place value chart

683.125 can be represented using the following place value chart.

Name of places of digits of decimal number 683.125

The digits 683 which are present on the 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 the 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 digit a moves one place to its right, the place value of the digit decreases. The 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 the right, its place value becomes $\frac{1}{1000}$ or one thousandths.

Reading the 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 the decimal part are read out with their place name of digits.

Examples of reading decimal numbers using place names

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 twenty five thousandths.

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 the decimal part separately.

Examples of reading decimal numbers with digit present

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.

Expanded form of decimals

The 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.

Examples of expanding a decimal number

Expand 45.682

45.682 can be represented in a place value chart of decimal numbers as follows.

Name of places of digits of decimal number 45.682

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

Expand 785.243

The place value of the chart of 785.243 is:

Name of places of digits of decimal number 785.243

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

Convert fractions to 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. The number of digits moved must be equal to the number of zeros in the denominator. After moving, put point '.' on the left of the last number reached.

Step 4: In case there are no more digits left on the left of '.', put an additional zero on the left of the '.'.

Examples of fractions into decimals

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 a 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

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 a 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

Convert decimals to 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. 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 the number of zeros after 1 equal to the number of decimal places present in the given decimal number.

Examples of decimals into fractions

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 the number of zeros after 1 equal to the number of decimal places present in 11.9, which is 1.

So, finally the fraction becomes $\frac{119}{10}$

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, the 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 two 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, the 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 five zeros after 1 in the denominator. $\frac{1189}{100000}$

Convert mixed fractions to 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.

Examples of mixed fractions into decimals

Convert $4 \frac{5}{10}$ into decimals.

Here, 4 is a whole number and $\frac{5}{10}$ is a fractional part. which is equal to 0.5

∴ $4 \frac{5}{10}$ is written as 4.5

Step 1: Write the whole number 4 and the decimal after 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

Convert $128 \frac{4}{100}$ into decimals.

Step 1: Write the whole number 128 and the decimal after 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 128.04

Example 3: Convert $1025 \frac{1}{10}$ into decimals.

Step 1: Write the whole number 1025 and the decimal after 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 1025.1

Solved Examples

Write the following decimals into words.

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

Write the following numbers in words to decimal numbers.

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

Write the decimal for the following expansions.

$40 + 5 + \frac{1}{10} + \frac{2}{100}$

= 45 + 0.1 + 0.02

= 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

Change the following decimal numbers into expansion form.

3.01

= 3 + 0.01

= $3 + \frac{1}{100}$
14.02

= 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

= $1 + \frac{5}{10000}$

Turn the following fractions into decimals.

$\frac{147}{100}$

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 7. 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 a whole part of 14 and a 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 the whole part 14. Write the decimal number 0.32, obtained in step 1, after the decimal. Finally the decimal number becomes 14.32
$16 \frac{484}{1000}$

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

Write the following decimals into fractions.

0.72

Step 1: Count the number of decimal places in 0.72, which are 2.

Step 2: After removing the decimal point, the 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, the 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, the number becomes 14789.

Write 14789 in the numerator. $\frac{14789}{_____}$

Step 3: Write digit 1 in the denominator. $\frac{14789}{1_____}$

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, the 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. $\frac{2019}{100}$