Decimals
Class 8
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.
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).
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
Addition of decimal numbers :-
Write the given decimal numbers one below the other such that decimal points of both numbers lie below each other, then add numbers as usual.
Subtraction of decimal numbers :-
Write the decimal number which is to be subtracted below the other number such that decimal points of both numbers lie below each other, then subtract numbers as usual.
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
Addition of decimal numbers :-
Write the given decimal numbers one below the other such that decimal points of both numbers lie below each other, then add numbers as usual.
Subtraction of decimal numbers :-
Write the decimal number which is to be subtracted below the other number such that decimal points of both numbers lie below each other, then subtract numbers as usual.