Decimal Fractions
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Decimal Fractions
Concept Fractions in which denominations are powers of 10 are decimal fractions. 1 /10 = 0.1, 1 / 100 = 0.01
Conversion of Decimal into fraction:eg: 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 porducts= 6.3204*100 = 632.04
3.2.61*1.3=261*13=3393 some of decimal places 2 +1 =3 = 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 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
Concept Fractions in which denominations are powers of 10 are decimal fractions. 1 /10 = 0.1, 1 / 100 = 0.01
Conversion of Decimal into fraction:eg: 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 porducts= 6.3204*100 = 632.04
3.2.61*1.3=261*13=3393 some of decimal places 2 +1 =3 = 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 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
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