DECIMAL FRACTIONS
Definitions
1. Decimal fractions – Fractions in which the denominators are powers of 10 are
called decimal fractions.
Examples :
,
,
,
etc.
These fractions are written by using decimal points (.) respectively-0.2, 0.02,
0.005, 0.0007 etc.
The figure which is left from decimal point in decimal fraction is called
characteristic and the figure which follow the decimal point is called mantissa.
The figure right of decimal point is always less than one. In reading a decimal,
the digits are named in order.
Example : 25.458 is read as twenty five point four, five, eight (with stress on the
last number).
2. Place value of number in decimal- The first digit followed by decimal is called
tenth, the second digit is called hundredth place and the third digit is called
thousandth place
In 0.1, the place value of 1 is =
In 0.01, the place value of 1 is =
In 0.001, the place value of 1 is =
The place valued table is given below :
Thousand
Hundred
Tens
Unit
(1000)
(100)
(10)
(1)
Tenth
Hundredth
Thousandth
3. Conversion of decimals into vulgar fractions – Write down the given number
without the decimal point for the numerator, and for the denominator write I
followed by as many zeroes as many are there in digits after the decimal point.
Example : Change the number 2.345 in vulgar fraction.
Soln. The numerator of vulgar fraction = 2345. The number of digits which follow
the decimal point = 3.
denominator of vulgar fraction = 1000
2.345 =
=
=2
4. Conversion of a vulgar fraction into a decimal fraction :
(A) Change of denominator in the multiple of 10.
Example : =
(B)
By division method – By this method, conversion of vulgar fraction into
decimal fraction has to be completed in three steps
a)
Numerator of given fraction is divided by denominator.
b)
Decimal point is given after Quotient when remainder is less than divisor,
Now place zero behind right side of remainder and by simple division method,
this increased remainder is again divided by divisor and quotients are placed
after decimal point
c)
If remainder remains again, then zero is placed again to right side of
remainder and division method is repeated. This process is continued till
remainder becomes zero otherwise process is stopped after three or four digits.
Example : Change
Soln.
to decimal fraction
5) 27 (5.4
-25
X 20
-20
XX
= 5.4 ; Ans.
5. Addition and subtraction of decimal – In addition or subtraction method of
decimal, numbers are arranged in columns row in such a way that decimal points
come just below the first decimal point, then addition or subtraction is done.
Example 1. Add 5.032, 0.8 and 40.
Soln. 5.032 + 0.8 + 40 = 45.832 ; Ans.
5.032
+ 0.800
+ 40.000
45.832
Example 2. Subtract 19.052 from 24.5
Soln. 24.5 – 19.052 = 5.448; Ans.
24.500
- 19.052
5.448
6. Multiplication of decimal with decimal : Multiplication of decimal with decimal
number is the same as simple multiplication method but after multiplication,
decimal point is placed at the position from the right, to the sum of the number of
digits in multiplier and multiplicand.
Example : Multiply 3.5 by 2.3
Soln.
3.5
× 2.3
105
70
8.05
Since, position of decimal in multiplicand = 1.
Position of decimal in multiplier = 1.
Position of decimal in product = 1 + 1 = 2.
3.5 × 2.3 = 8.05 Ans.
7. Division of decimal with whole number : Division of decimal with whole
number is done as follows :
Make number of digits right to decimal point equal in dividend and divisor. If they
are not equal then make them equal by placing zero(s). After this, simple division
process is adopted.
Example : Divide 15, 18 by 3.
Soln.
=
= 5.06; Ans.
Rule : There are two digits after decimal point as dividend is 15.18. So, two zero
are placed on diviser 3 and made equal. After this simple division is done.
Memorable Facts
1. There is no change in the value of number if we place zero at the end of
number after decimal point in any decimal fraction.
Example : 1.5 = 1.50 = 1.500, etc.
2. In any decimal fraction, if number of digits after decimal point in numerator
and denominator are the same then decimal point can be removed.
Example :
=
3. There is no significance of one or more zeros to the right of decimal point of
any characteristic (integer).
Example : 1.0, 2.00, 3.000 ….etc.
4. There is no significance of any zeros to the left of decimal point in decimal
fraction. Generally, we write zero for avoiding error.
Example : 6 = 0.6, 7 = 0.7 etc.