DECIMAL FRACTIONS

1.Decimal fractions: Fraction in which denominations are powers
of 10 are decimal fractions.

Example:1 /10 = 0.1, 1 / 100 = 0.01

2.Convertion of Decimal into fraction:-

Example: 0.25 = 25/100 = 1/4

3.i) If numerator and denominator contain same number of decimal
places, then we remove decimal sign. Thus, 1.84/2.99 =184/299


Problems

1.0.75 =75/100 =3/4


2.Find products= 6.3204*100
               = 632.04


3.2.61*1.3=261*13=3393 some of decimal places 2 +1 =3

sol: 3.393

4.If 1/3.718 =0.2689,then find value of 1/0.0003718 ?

Sol: 10000/3.718 =10000*1/3.718
                 =10000*0.2689
                 = 2689

5.Find fractions :

i) 0.37 = 37/99
ii)3.142857 =3+0.142857
            =3 +142857/999999
            = 3 142857/ 999999 
iii) 0.17=17-1/90 =16/90=8/45
iv)0.1254 =1254 -12/9900 =1242/9900=69/550

6.Fraction 101 27/100000

Sol: 101+27/100000
      =101+0.00027
      =101.00027

7.If 47.2506 =4A + 7/B +2C + 5/D + 6E then 40+7+0.2+0.05+0.0006

Sol: comparing terms 
        4A= 40 => A=10
 7/B = 7 => B=1
 2C= 0.2=> C=0.1
 5/D= 0.05=>D=5/0.05 =>5*100/5 =100
 6E= 0.0006=> E= 0.0001
 5A + 3B+6C+ D+ 3E = 5*10+ 3*1+ 6*0.1 + 100+ 3*0.0001
                   =50+3+0.6+100+0.0003
                          =153.6003
                                              
8.4.036 divided by 0.04

Sol: 4.036/0.04 =4036/4 =100.9

9.[ 0.05/0.25 + 0.25/ 0.05]3

Sol: =>[5/25 + 25/5] 
     = [1/5+ 5]3
     =26/53
     =5.23
     = 140.603

10.The least among the following :-
a. 0.2 b.1/0.2 c. 0.2 d. 0.22

sol:10/2 =5    0.2222      0.04 0.04 < 0.2 < 0.22 --------<5
Since 0.04 is least (0.2)2 is least.

11.Let F= 0.84181

Sol: when F is written as a fraction in lowest terms, denominator 
exceeds numerator by 
84181 -841 /99000 = 83340/99000 =463/550
Required distance = (550 – 463) = 87

12.2 .75 + 3.78

Sol: [-2+0.75]+[-3+0.78]
     =-5+[0.75+0.78]
     = -5+1.53
     =-5+1+0.53
     = -4+0.53
     = 4.53

13.the sum of first 20 terms of series is 1/5*6 +1/6*7+1/7*8-----

Sol: [1/5 -1/6]+[1/6-1/7]+[1/7-1/8]+------------------------
        = [1/5-1/25]
        =4/25=0.16

14.13 +23+ ------------+93 =2025

Sol: value of (0.11) 3+ (0.22) 3+---------(0.99)3 =>
(0.11) [1+2+--------+9]
        =0.001331*2025
        =2.695275

15.(0.96)3 – (0.1)3/ (0.96)2 +0.096 +(0.1)2

Sol: formula => a3 -b3/a2 +ab +b2 =a -b
(0.96-0.1)=0.86

16.3.6*0.48*2.50 / 0.12*0.09*0.5

Sol: 36*48*250/12*9*5=800

17.find x/y = 0.04/1.5
            = 4/150 =2/75
  find y-x/y+x 
 (1- x/y) / (1+ x/y) 
 1 - 2/75 /1 +2/75 =73/77

18.0.3467+0.1333

Sol: 3467 -34/9900 + 1333-13/9900
 = 3433 +1320/9900
 = 4753/9900
 = 4801 -48/9900 =0.4301