## Decimals

Decimals :-

Observe below number

382.724
1st part = 382 = integral part
2nd part = .724 = decimal part

The small dot in between the digits 2 & 7 is called decimal point. Such a number is called Decimal Point.

Hundreds
(100)
Tens
(10)
Ones
(1)
Tenths
(1/10)
Hundredths
(1/100)
Thousandths
(1/1000)
Number
3     8     2      7         2            4 382.724

Expanded Form :-

382.724 = 3 x 100 + 8 x 10 + 2 x 1 + 7 x (1/10) + 2 x (1/100) + 4 x (1/1000).

Position after decimal point Represents Called
First position after decimal point Tenths First decimal place
Second position after decimal point Hundredths Second decimal place
Third position after decimal point Thousandths Third decimal place

Like and Unlike decimal Numbers :-

Decimal Numbers :- The decimal numbers having equal number of decimal places. e.g. 2.11, 584.72,

Unlike Decimal Numbers :- The decimal numbers having different number of decimal places. e.g. 4.2, 312.011,

Comparison of decimal numbers :-

1) Express given decimal numbers as like decimal numbers.
2) The decimal number having greater whole number part is greater.
3) If whole number part is equal, compare tenth digits- the number having greater tenth digit is greater.
If thenth digits are equal, compare digits at hundredths place- the number having greater hundredth digit is greater.

e.g  find which number is greater?
319.72 , 319.75

1)These are like decimal numbers & whole number parts are equal.
2) Compare tenth digits. In both numbers, digit at thenths place = 7
3)Compare hundredth digits.
In 319.72, digit at hundredths place = 2
In 319.75, digit at hundredths place = 5
since 5 > 2, hence 319.72 < 319.75