Decimal Numbers

A number whose whole number part and fractional part is separated by a decimal point is known as a decimal number.               

A dot (.) represents a decimal point.

When the numbers are expressed in the decimal form are called decimal numbers.

In a decimal number decimal point separates the whole number part and the fractional part.

 Example: We see a number

35 . 4 

The number is “thirty five and four tenths” the decimal point is written between Ones and Tenths.

Number 35.4 has 3 Tens, 5 Ones, and 4 tenths.

 Place Value  

In decimal number system each digit has a value depending on the place of the digit in a number is known as the place value of the digit.

 When numbers move right from the decimal point, 
 each place value is divided by 10.

Example: The first digit after the decimal represents the tenths place. 5.4

The second digit after the decimal represents the hundredths place. 3.62

The third digit after the decimal represents the thousandths place. 4.237

We continue it for the remaining digits to fill in the
place values until there are no digits left. 

Relationship between decimal number and fractions.

 A unit is represented by 1.

 1 unit divide into 10 equal parts = 1/10 = 0.1 = Tenths

 1 unit divide into 100 equal parts = 1/100 = 0.01 = Hundredths

 1 unit divide into 1000 equal parts = 1/1000 = 0.001 = Thousandths

How to read decimal numbers

Let’s start to read the whole number 573 read as

               “five hundred seventy three”

now we read number 23,684

“twenty three thousand six hundred eighty four”

note that to read above numbers we don’t mention word and anywhere.

             a decimal number 6.5 read as

                    “six and five tenths”

24.3

                    “twenty four and three tenths”

three and twenty six hundredths

24.356

twenty four and three hundred fifty six thousandths 

notice that we read and for decimal point, but in our daily life usually we read a decimal point as 

 6.5 

six point five             

3.26

                       three point two six

another way to write a decimal number

Example:                  135.624

We read this decimal number as one hundred thirty five and six hundred twenty four thousandths.           

The right part of the decimal point, six hundred twenty four thousandths, can be written as a fraction form 624 over 1000.

135  624/1000

but we hardly see that a decimal number   
written like this.

Note- When a decimal number is less than 1(one), write a zero in the ones place.

Example: write 0.235  not .235

How to write these numbers in decimal form.

(1)   five hundred twenty six and four tenths.

 526.4 

(2)    (3×10) + (5×1) + (2×1/10) + (4×1/100)

35.24

(3)  four hundred thirty seven thousandths.

 0.437 

(4) three hundred and thirty seven thousandths.

300.037

(5)   two and forty five hundredths or 

                       two point four five.

  2.45 

(6)seventy one and four hundred fifty six thousandths.                           

                           71.456

 We see the numbers in place value table. 

	Tens (10)	Ones    (1)	Tenths   (1/10)
3 . 5	0	3	5
24.3	2	4	3
56 . 7	5	6	7

MILLONS	HUNDRED THOUSANDS	TEN THOUSANDS	THOUSANDS	HUNDREDS	TENS	ONES	DECIMAL POINT	TEN T H S	HUNDRED T H  S	THOUSAND T H  S
5	4	1	2	7	6	3	.	2	7	9