Decimal Number Place Value System : Introduction.

PLACE VALUE SYSTEM FOR DECIMAL NUMBERS:

A Decimal Number can be defined as a number whose whole number part and the fractional part is separated by a decimal point.

The dot in a decimal number is called Decimal Point.

The numbers written on the right side of a decimal point are parts of  whole numbers, called Decimal Places.

The first digit after the decimal point represents the Tenths(th) place.The next digit after ‘Tenths(th)’ place represents Hundredths(h) place.The next digit after ‘Hundredths(h)’ place Thousandths(th) place.Like wise all the digits continue to fill in the place values until no digits left.  

Word Form or Number Name: 

The place values after the decimal point are written as:

The decimal place number names ends with “ths” , the number names are denoted by small letters.

The below table represents the decimal place value number name in Indian and International place value systems:

DECIMAL NUMBER	FRACTION	PLACE VALUE  NUMBER NAME
		Indian System	International System
0.1 0.6	1/10 6/10	Tenths (t) Six-Tenths	Tenths (t) Six-Tenths
0.01 0.03	1/100 3/100	Hundredths (h) Three-Hundredths	Hundredths (h) Three-Hundredths
0.001 0.008	1/1000 8/1000	Thousandths (th) Eight-Thousandths	Thousandths (th) Eight-Thousandths
0.0001 0.0005	1/10000 5/10000	Ten-Thousandths (tth) Five-TenThousandths	Ten-Thousandths (tth) Five-TenThousandths
0.00001 0.00004	1/100000 4/100000	Lakhths (l) Four-Lakhths	Hundred-Thousandths (hth) Four-HundredThousandths
0.000001 0.000002	1/1000000 2/1000000	Ten-Lakhths (tl) Two-TenLakhth	Millionths (m) Two-Millionth
0.0000001 0.0000006	1/10000000 6/10000000	Croreths ( c ) Six-Croreth	Ten-Millionths ( tm ) Six-TenMillionth

The place value number names for the decimal numbers are same up to Ten-Thousandths place value in Indian/ Hindu-Arabic and International place value system.

The place value number names differs from  the Ten-Thousandths in both the place value systems.

PLACE VALUE CHART :

1. INDIAN / HINDU-ARABIC PLACE VALUE SYSTEM:

2. INTERNATIONAL PLACE VALUE SYSTEM:

Place Value : Indian (vs) International system for 6 Digits

INDIAN (VS) INTERNATIONAL PLACE VALUE SYSTEM FOR 6 DIGIT:

 Q.2:  900001

Solution:

INDIAN PLACE VALUE SYSTEM	INTERNATIONAL PLACE VALUE SYSTEM
1.Expanded  Form:    900001 = 9,00,000 + 0 + 0 + 0 + 0 + 1.    = 9,00,000 + 1 .                                  (or)    900001 = 9 Lakhs + 1 One.      2. Number : 9,00,001. 3. Word Form (or) Number Name :      Nine Lakh and one.	1.  Expanded Form :      900001 = 900,001 + 0 + 0 + 0 + 0 + 1 .      = 900,001 + 1 .                     (or)      900001 = 9 HundredThousands + 1 One. 2. Number : 900,001. 3. Word Form (or) Number Name:      Nine Hundred Thousand and one.

NOTE: We can leave out the digit 0 while writing the expanded form.

4. Place Value Chart:

4.1. INDIAN (OR) HINDU-ARABIC SYSTEM: 

PERIOD	CRORES		LAKHS		THOUSANDS		ONES
PLACE VALUE	TC	C	TL	L	TTH	TH	H	T	O
NUMBER				9	0	0	0	0	1

 

4.2. INTERNATIONAL SYSTEM:

PERIOD	MILLIONS			THOUSANDS			ONES
PLACE VALUE	HM	TM	M	HTH	TTH	TH	H	T	O
NUMBER				9	0	0	0	0	1

Place Value : Indian (vs) International system for 7 digits

INDIAN (VS) INTERNATIONAL PLACE VALUE SYSTEM FOR  7 DIGITS :

Question : 1655634

Solution:

INDIAN PLACE VALUE SYSTEM

INTERNATIONAL PLACE VALUE SYSTEM

1.Expanded  Form:   1655634 = 10,00,000 + 6,00,000 +                          50,000 + 5,000 + 600 + 30                      + 4.                    ( or )    1655634 = 1 TenLakhs + 6 Lakhs + 5                             Tenthousands + 5 Thousands                      + 6 Hundreds + 3 Tens +                       4 Ones .        2. Number : 16,55,634. 3. Word Form (or) Number Name :      Sixteen Lakh fifty-five Thousand six      Hundred and thirty-four.

1.  Expanded Form :      1655634 = 1,000,000 + 600,000 + 50,000 +                           5,000  + 600 + 30 + 4 .                       ( or )      1655634 = 1 Millions + 6 Hundred Thousands +                         5 Ten Thousands + 5 Thousands +                         6 Hundreds + 3 Tens + 4 Ones .          2. Number : 1,655,634. 3. Word Form (or) Number Name:      One Million six Hundred fifty-five Thousand six            Hundred and thirty-four .

 4. Place Value Chart:

4.1. INDIAN (OR) HINDU-ARABIC SYSTEM: 

PERIOD	CRORES		LAKHS		THOUSANDS		ONES
PLACE VALUE	TC	C	TL	L	TTH	TH	H	T	O
NUMBER			1	6	5	5	6	3	4

4.2. INTERNATIONAL SYSTEM:

PERIOD	MILLIONS			THOUSANDS			ONES
PLACE VALUE	HM	TM	M	HTH	TTH	TH	H	T	O
NUMBER			1	6	5	5	6	3	4

Place Value - Indian (vs) International System - 9 digits.

INDIAN (VS) INTERNATIONAL PLACE VALUE SYSTEM:

Let the number be:  834615792

INDIAN PLACE VALUE SYSTEM

INTERNATIONAL PLACE VALUE SYSTEM

1. In this system, the digits are grouped into  2  place values from THOUSANDS periods and  3 place values in ONES period. i.e;  ONES( H , T, O)        THOUSANDS ( TTh, Th)        LAKHS   ( TL , L) CRORES ( TC, C ) 2.Expanded Form: 80,00,00,000 + 3,00,00,000 + 40,00,000 + 6,00,000 + 10,000 + 5,000 + 700 + 90 + 2.                     OR 8 Ten Crore +  3 Crore + 4 Ten Lakh + 6 Lakh + 1 Ten Thousand + 5 Thousand +7 Hundred + 9 Ten + 2 One. 3.  Number :  83,46,15,792. 4.Word Form (OR) Number Name :  Eighty-three crore forty-six lakh fifteen    thousand seven hundred and ninety-two.

1.      In this system, the digits are grouped into 3 place values in  the periods .   i.e;  ONES ( H, T, O)        THOUSANDS ( HTh, TTh Th )         MILLIONS ( HM , TM, M )        2. Expanded Form:  800,000,000 + 30,000,000 + 4,000,000  +  600,000 + 10,000 + 5,000 + 700 + 90 + 2.                            OR 8 Hundred Million + 3 Ten Million + 4 Million + 6 Hundred Thousand +      1 Ten Thousand + 5 Thousand  +             7 Hundred + 9 Ten + 2 One . 3. Number : 834,615,792. 4. Word Form (OR) Number Name : Eight hundred thirty-four million six hundred fifteen thousand seven hundred and ninety-two.

           

PLACE VALUE CHART:

1. INDIAN (OR) HINDU-ARABIC SYSTEM:  

PERIOD	CRORES		LAKHS		THOUSANDS		ONES
PLACEVALUE	TC	C	TL	L	TTh	Th	H	T	O
NUMBER	8	3	4	6	1	5	7	9	2

2. INTERNATIONAL SYSTEM:

PERIOD	MILLIONS			THOUSANDS			ONES
PLACE VALUE	HM	TM	M	HTh	TTh	Th	H	T	O
NUMBER	8	3	4	6	1	5	7	9	2