Decimal

 Decimal Fractions :

Fractions a/b in which the denominators are powers of 10 are called decimal fraction .

1/10, 1/100, 1/1000 etc. are respectively the tenth ,hundredth, and thousandth part of 1 .

6/10 is 6 tenths, written as 0.6 (called decimal 6 )

19/100 is 19 hundredths written as 0.19 ( called decimal one nine )

13/100 is 13 hundredths written as 0.13 ( called decimal one three )  

1/100 is 1 hundredths written as 0.01 (called decimal zero one )

122/100 is 122 hundredths written as 1.22 ( called one decimal two two)

Example :

1) what is eighty-five hundredths in a fraction ?

Solution :

1/100 is hundredth part of 1 ,

We can write eighty-five hundredths in a fraction 85/100.

2)What is 8 hundredths ?

Solution :

1/100 is hundredth part of 1,

We can write 8 hundredths in fraction 8/100.

Convert a Decimal Into a fraction :

Rule :

In the denominator, put 1 under the decimal point and annex with it as many zeros a as is the number of digits after the decimal point. Now , remove the decimal point and reduce the fraction to lowest terms.

Example : 

1. convert i) 0.98     ii) 3.004 into  fractions.

Solution :

i) 0.98 = 98/100  = 49/50

ii) 3.004 = 3004/1000

Remark : Annexing zeros to the extreme right of a decimal fraction does not change its value .

Thus, 0.3 = 0.30 = 0.300 etc .

Addition & Subtraction of Decimal fractions :

Rule :

The given numbers are so placed each other that the decimal point lie in column . Now, the numbers can be added or subtracted as usual, putting the decimal point under the decimal points.

Example :

2 i) 61.3 + 5.079 + 0.38 + 0.5= ?

Solution:

61.3

  5.079

  0.38

+0.5

-----------

57.259

-----------

ii) 5.063 - 3.87 =  ?

Solution :

  5.063

- 3.87

----------

  1.193

----------

iii)  0.34 - 0.09= ?

 0.34

-0.09

----------

 0. 25

----------

iv) 5.063 + 3.87 = ?

  5.063

+3.87

------------

  8.933

------------

Multiplication of a Decimal Fraction by a power of 10 :

Rule :

 Shift the decimal  point to the right by as many places of decimal as is the power of 10 .

Example :

i)3.4207 X 100

Solution:

342.07 9 (shift decimal 2 places to the right )

ii)0.0375 X 1000

Solution :

37.5 ( Shift the decimal 3 places to the right )

iii) 0.005 X 1000

Solution :

50.00

iv) 0.05 X 100

Solution :

25.00

v) 234.3 X 100

Solution:

23430.0

Multiplication of two or More Decimal fractions :

Rule :

Multiply the given numbers considering them without the decimal point. In the product,the decimal point is marked off to obtain as many places of decimal as is the sum of the number of decimal places in the given numbers .

Example :

i) 2.5143 X 1.1

Solution :

=276573

Sum of decimal places = 4 + 1 = 5

=2.76573

ii)2 X .2 X .02 X 0.0002

Solution:

=16

Sum of decimal places = 6

=0.000016

iii) .7 X .2 X .02 =

Solution :

=28

Sum of decimal places =4

=0.0028 

iv) 3.71 X 1.21 =

Solution :

=44891

Sum of decimal places = 4

4.4891

Divide a Decimal Fraction by a Counting Number :

Rule :

Divide the given decimal fraction without the decimal point by the given counting number. Now, in the quotient, put the decimal point to give as many places of decimal as are there in the dividend.

Example:

i) 0.64÷8    ii) 0.135÷15    iii) 0.000225÷15

Solution:

i) 64/8 =8 so that 0.64/8 = 0.08

ii) 0.135/15= 0.009

iii) 0.000225/15 = 0.000015

Divide a Decimal Fraction by a Decimal Fraction

Rule:

Multiply both the dividend and the divisor by a suitable power of 10 to make the divisor a whole number. Now proceed as above .

Example :

i) 49÷0.07    ii) 0.00121÷0.11    iii) 0.000256÷0.16

Solution:

      49         49×100              4900

 i) ------- = ----------------- =  -------------- = 700 

     0.07       0.07×100             7

         

     0.00121             0.00121 X 100                        0.121

ii) --------------- = ------------------------------- = ------------------------------- = 0.011

     0.11                    0.11 X 100                                11

      0.000256                 0.000256 X 100                    0.0256

iii) -------------------- = -------------------------------- =---------------------------------- = 0.0016

       0.16                         0.16 X 100                            16 

L.C.M. & H.C.F. of Decimal Fractions :

Rule :

In  the given decimal numbers, make same number of decimal places by annexing zeros if needed. Considering these numbers without decimal places, find L.C.M. or H.C.F. as the case may be. Now, in the result, mark off as many decimal places as are there in each of the given numbers .

Example :

Find the L.C.M. & H.C.F. of 1.75, 5.6 and 7.

Solution:

L.C.M. of 1.75, 5.60, 7.00 is 28.00

H.C.F. of 1.75, 5.60, 7.00 is 0.35

In Decimal Comparison of Fractions:

Rule:

Convert the given fractions in decimal form. Now arrange them in ascending or descending order as per requirement.

Example:

Arrange 2/3, 7/12, 3/8, and 16/25 in ascending order.

Solution:

2/3=0.666; 7/12= 0.583; 3/8=0.375 and 16/25= 0.640

it means

0.375<0.583<0.640<0.666

3/8 < 7/12 < 16/25 < 2/3

 

Exercise

1) If 12276÷1.55 = 7920,the value of 122.76 ÷15.5 is :

a)7.092    b)7.92    c)79.02    d) 79.2

2) 0.39393939.... is equivalent to the fraction :

a) 39/100    b) 93/99    c) 93/100    d) 39/99

3)The fraction for the recurring decimal 0.53535353... is 

a) 26/53    b) 27/53    c) 28/53    d) 53/99

Answer

1) b    2)     3) d    4) d