Post on 31-Mar-2018
19
04. Ëþktþ yÃkqýkOf, Ëûkktþ yðÞð 0.5, 1.5, -2.5, .... ðøkuhu MktÏÞkykuLku Ëþktþ yÃkqýkOf fnu Au.
heík Lkt. 1 :
Ëþktþ yÃkqýkOfLku MkkËk yÃkqýkOf{kt YÃkktíkrhík fhðk.
(i) 353.510
(ii) 2752.75100
LkkUÄ: òu Ëþktþ ÃkAe yuf MktÏÞk nkuÞ íkku 10, çku MktÏÞk nkuÞ íkku100, ºký MktÏÞk 1000, .... yu{ AuË{kt ÷¾e, ytþLkeMktÏÞk{ktÚke Ëþktþ fkZe Lkk¾ðwt.
heík Lkt. 2 :
MkkËk yÃkqýkOfLku Ëþktþ{kt YÃkktíkrhík fhðk.
(i) 537 5.37100
(ii) 67 0.067
1000
LkkUÄ : òu AuË{kt10 nkuÞ íkku yuf{Lke MktÏÞk Ãknu÷kt Ëþktþ ,100 nkuÞ íkku ËþfLke MktÏÞk Ãknu÷k Ëþktþ {qfðwt.1000 nkuÞ íkku MkkuLke MktÏÞk Ãknu÷k Ëþktþ {qfðwt.
heík Lkt. 3 :
Ëþktþ yÃkqýkOf Lkk Mkhðk¤k - çkkËçkkfe fhðk.(i) 5.064 + 3.98 + 0.7636 + 2
= 5.0640 + 3.9800 + 0.7636 + 2.000
11.8076
(ii) 13-5.1967
13.000 5.1967 7.8033
LkkUÄ: Ëþktþ yÃkqýkOfLkk Mkhðk¤k çkkËçkkfe fhðk Ëþktþ ÃkAeLkkytfLke MktÏÞk Mk{kLk fhe økýíkhe fhðe. ytf Mk{kLk fhðk ËþktþÃkAe sYhe þqLÞ {wfðe.
heík Lkt. 4 :
Ëþktþ yÃkqýkOfLkk økwýkfkh fhðk.(i) 43.28 × 10 = 432.8(ii) 2.61 × 1.3 = 261 × 13 = 3393 = 3.393LkkUÄ: ykÃku÷ Ëþktþ yÃkqýkOfLkk økwýkfkh fhðk {kxu Mkki«Úk{ ykÃku÷
MktÏÞk{ktÚke Ëþktþ ¼q÷e sðk, íÞkhçkkË Ëþktþ ÃkAeLke MktÏÞkøkýe íkuLku Mkhðk¤ku fhe {¤u÷ sðkçk{kt Mkhðk¤k sux÷k Ëþktþ
{qfðk.heík Lkt. 5 :
Ëþktþ yÃkqýkOfLkk ¼køkkfkh fhðk.LkkUÄ: Ëþktþ yÃkqýkOf MktÏÞkykuLkk ¼køkkfkh fhðk íku MktÏÞkyku{ktÚke
Ëþktþ r[LnT fkZe Lkk¾e {¤u÷ MktÏÞkLkk ¼køkkfkh fhðkíÞkhçkkË ¼køkV¤Lke MktÏÞk{kt ytþ yLku AuËLke MktÏÞk{kt Ëþktþr[LnT ÃkAeLke MktÏÞkLke çkkËçkkfeLku ykÄkhu ¼køkkV¤{kt Ëþktþ
r[LnT {wfðwt. òu çkkËçkkfe ÄLk nkuÞ íkku ¼køkV¤{kt AuÕ÷uÚke íkux÷kytf ÃkAe Ëþktþ r[LnT {wfðwt. òu çkkËçkkfe Éý nkuÞ íkku sux÷kÉý ÃkqýkOf nkuÞ íkux÷e þqLÞ ¼køkV¤{kt {qfðe.
WËk.: (i) 0.063 0.9
63 9
7 (ytþLkk ºký Ëþktþ – AuËLkk yuf
Ëþktþ = çku Ëþktþ)
0.07 sðkçk
(ii) 0.75 0.025
75 25
3 (ytþLkk çku Ëþktþ – AuËLkk ºký
Ëþktþ = Éý yuf Ëþktþ)
30 sðkçk
«uõxeMkLkk Ëk¾÷kyku :1. Lke[uLkk Ëþktþ yÃkqýkOfLku MkkËk yÃkqýkOf{kt Vuhðku.
01.70.007
1000
02.15815.810
03.270.27
100
04.80.08
100
05.20.0002
10000
2. Lke[uLkk Ëþktþ yÃkqýkOfLku MkkËk yÃkqýkOf{kt Vuhðku.
01.2 2 25 5 2
4 0.410
02.3 3 52 2 5
15 1.510
20
03.8 8 425 25 4
32 0.32100
04.7 7 254 4 25
175 1.75100
05.11 125 118 125 8
1375 1.3751000
06.3 8 3
125 125 8
24 0.024
1000
3. Lke[uLke MktÏÞkykuLku [Zíkk ¢{{kt økkuXðku.
1 2 4 3 5 6, , , , ,3 5 7 5 6 7
WÃkhLke Ëhuf MktÏÞk{kt çku Ëþktþ MkwÄe ¼køkkfkh fhðk
1 2 4 = 0.33, = 0.40, = 0.573 5 73 5 6 = 0.60, = 0.83, = 0.855 6 7
íkuLkk ËþkOþ {qÕÞLku ykÄkhu [Zíkk ¢{{kt 1 2 4 3 5 6, , , , ,3 5 7 5 6 7
4. Lke[uLke MktÏÞkykuLku Wíkhíkk ¢{{kt økkuXðku.
13 15 17 7, , ,16 19 21 8
13 0.8116
,15 0.7819
, 17 0.8021
,7 0.878
íkuLkk ËþkOþ {qÕÞLku ykÄkhu Wíkhíkk ¢{{kt 7 13 17 15, , ,8 16 21 19
5. Lke[uLkk Ãkife MkkiÚke LkkLke MktÏÞk þkuÄku.
5 7 8 11, , ,9 11 15 17
5 70.55, 0.639 11 ,
8 110.53, 0.6415 17
MkkiÚke LkkLke MktÏÞk 8
15
6. Lke[uLkk Ãkife MkkiÚke {kuxe MktÏÞk þkuÄku.
(i)1 23 11 17, , ,4 24 12 24
1 0.254 ,
23 0.9524
11 0.9112
,17 0.7024
Ëþktþ {qÕÞLku ykÄkhu Mkk iÚke {kuxe MktÏÞk 2324
(ii)1 2 3 4, , ,2 3 4 5
1 0.502 ,
2 0.663
3 0.754 4 0.80
5
Ëþktþ {qÕÞLku ykÄkhu Mkk iÚke {kuxe MktÏÞk 45
07. 337.62 8.591 34.4 (?)
337.620 8.591 34.400
380.611
08. 1 0.1 0.01 0.001 Lke ®f{ík þkuÄku.
1 0.100 0.010 0.001
1.111
09. 34.95 240.016 23.98 (?)
34.950 240.016 23.980
298.946
21
10. 617 6.017 0.617 6.0017 _____
617 6.017 0.617 6.0017
629.6357
11. 48.95 32.006 _____
48.950 32.006
16.944
12. 792.02 101.32 306.76 ______
893.34 306.76
586.58
13. 12.1212 17.0005 9.1102 _______
29.1217 9.1102
20.0115
14. 892.7 573.07 95.007 ______
319.63 95.007
224.623
15. 3889 12.952 (?) 3854.002
3901.952 (?) 3854.002
(?) 3854.002 3901.952
47.95
47.95
16. 138.009 341.981 146.305 123.6 (?)
333.685 123.6 (?)
(?) 333.685 123.6
(?) 210.085
17. 63.14 10 (?)
314 1000000100
314 10000
4314 10 yÚkðk 3140000
18. 518,000,000 Lku «{krýík MðYÃk{kt ÷¾ku.
518 10000006 8518 10 5.18 10
19. 0.000006723 Lku «{krýík MðYÃk{kt ÷¾ku.
9 66723 6723 10 6.723 101000000000
20. 0.002 0.5 (?)
0.0010 0.001
21. 0.014 0.014
0.000196
22. òu 1.125 10 0.001125k nkuÞ íkku k Lke ®f{ík þkuÄku.
1.125 10 0.001125k
11251.125 101000000
k
1125 1000101000000 1125
k
1101000
k 310 10k
3k
23. 16.02 0.001 (?)
0.01602
24. 0.04 0.0162 0.1 (?)
0.0000648
25. 3 0.3 0.03 0.003 30 Lke ®f{ík þkuÄku.
3 3 33 3010 100 1000
81 3 243100000 100000
0.00243
26.230.006255
Lkwt MkkËwYÃk ykÃkku.
625 23100000 5
0.02875
22
27. 0.3333 0.25 0.499 0.125 24 Lkw t MkkËwYÃk MkkËk
yÃkqýkOf{kt Vuhðku.
0.3333 0.25 0.499 0.125 24
0.1247376
28. 0.213 0.00213 (?)
213 1000001000 213
100
29. 4.036 0.04 (?)
4.0360.04
4036 1001000 4
100.9
30.1
0.04 Lkwt MkkËwYÃk ÚkkÞ.
1 100 250.04 4
31.3
30.05 0.25 (?)0.25 0.05
30.05 1.250.25
31.300.25
3 3
2130 26 5.225 5
3 3 5.2 (?)
5.2 ?
32. 0.04 (?) 0.000016
0.000016(?)0.04
16 100
1000000 4
4 0.0004
10000
33.0.009 0.1
(?)
0.009(?)0.1
? 0.09
34.144 14.4
0.144 x {kt (?)x
144 144 110 1000 144
x
0.0144x
35. 8.7 [7.6 {6.5 (5.4 4.3 2)}] Lkwt MkkËwYÃk
8.7 [7.6 {6.5 (5.4 2.3)}]
8.7 [7.6 {6.5 3.1}]
8.7 [7.6 3.4]
8.7 4.2
4.5
36.1 135.7 3 21 13 2
3 2
Lke ®f{ík þkuÄku.
1 135.7 3 210 53 2
3 235.7 3 210 5
33 1235.710 5
33 2435.710
[35.7 0.9]
34.8
23
37.3.6 0.48 2.500.12 0.09 0.5
Lke ®f{ík þkuÄk u.
36 48 25 100 100 1010 100 10 12 9 5
4 4 5 10
800
38.0.0203 2.92 (?)
0.0073 14.5 0.7
203 292 10000 10 1010000 100 73 145 7
4 = 0.85
39.5 1.6 2 1.4 (?)
1.3
8 2.8 5.2 41.3 1.3
40. 1(0.2 0.2 0.01)(0.1 0.1 0.02) Lke ®f{ík þkuÄk u.
0.2 0.2 0.010.1 0.1 0.02
0.04 0.010.01 0.02
0.050.03
53
41. (4 .7 13.26 4.7 9.43 4.7 77.31) L k e
®f{ík þkuÄku.
62.322 44.321 363.357 470
yLk u
= 4.7 (13.26 + 0.43 + 77.31)= 4.7 (100) = 470
42.0.896 0.763 0.896 0.2370.07 0.064 0.07 0.936
Lke ®f{ík þkuÄku.
0.896 (0.763 0.237)0.07 (0.064 0.936)
0.896 1.0000.07 1.000
12.8
43. 2 2(68.237) (31.763) (?)
2 2[ ( )( )]a b a b a b
(68.237 31.763)(68.237 31.763)
(36.474)(100)
3647.4
44.2 2(2.39) (1.61) (?)
2.39 1.61
(2.39 1.61)(2.39 1.61)2.39 1.61
2.39 1.61
4.00 4
45.2 2(2.644) (2.356) (?)
0.288
(2.644 2.356)(2.644 2.356)0.288
(0.288)(5.00)0.288
5.00 5
46. 2 2
5.32 56 5.32 44(7.66) (2.34)
5.32(56 44)(7.66 2.34)(7.66 2.34)
5.32(100)5.32(10.00)
10010
10
47.2 2(0.137 0.098) (0.137 0.098)
0.137 0.098
4
24
48.2 2(36.54) (3.46) 40(?)
(36.54 3.46)(36.54 3.46)(?)40
(33.08)(40)
(40) (?) 33.08
49. (7.5 7.5 37.5 2.5 2.5) (?)
2 2[(7.5) 2(7.5)(2.5) (2.5) ]
2 2( 2 )a ab b {wsçk,
2[7.5 2.5]
2[10.0] 100
50.2 2(2.697 0.498) (2.697 0.498)
2.697 2.697 0.498 0.498
Lke ®f{ík þkuÄk u.
2
«uõxeMkLkk Ëk¾÷k
1. Lke[uLkk{ktÚke õÞku yÃkqýkOf MkkiÚke LkkLkku Au ?
(y) 56
(çk) 79
(f) 35
(z) 23
2. Lke[uLkk [kh yÃkqýkOfku{ktÚke õÞku yÃkqýkOf 715
Úke ðÄw Au ?
(y) 35
(çk) 13
(f) 620
(z) 18
3. Lke[uLkk{ktÚke õÞku Lktçkh MkkiÚke {kuxku Au ?
(y) 10099
(çk) 99100
(f) 101100
(z) 100101
4.4 9 87 + + +
10 100 1000 Lkwt Mk{íkwÕÞ Ëþ{÷ð Au ?
(y) 7.21 (çk) 2.8 (f) 7.498 (z) 0.74985. yuf øk¤kLkk nkhLkwt ðsLk 25 økúk{, 35 {e÷e økúk{, yuf
çktøkzeLkwt ðsLk 15 økúk{, 5 r{÷e økúk{ yLku yuf ðexeLkwt ðsLk
10 økúk{, 450 r{÷e økúk{ Au. ËkøkeLkkykuLkwt fw÷ ðsLk Au ?
(y) 40.300 økúk{ (çk) 50.85 økúk{
(f) 50.49 økúk{ (z) 45.130 økúk{
51.3 3
2 2
(0.051) (0.041)(0.051) 0.051 0.041 (0.041)
2 2
2 2
[(0.051 0.041){(0.051) 0.051 0.41 (0.041) }](0.051) 0.051 0.041 (0.041)
0.051 0.041 0.092
52.3 3
2 2
(8.94) (3.56)(8.94) (8.94)(3.56) (3.56)
2 2
2 2
(8.94 3.56)[(8.94) (8.94)(3.56) (3.56) ](8.94) (8.94)(3.56) (3.56)
8.94 3.56 5.38
6. MktÏÞk 6, 4, 2, 1 yLku 0 Lku {kºk yuf s ðkh WÃkÞkuøk{kt
÷R 5 ytfkuLke MkkiÚke LkkLkk{kt LkkLke MktÏÞk çkLkþu ?(y) 12460 (çk) 01246(f) 61024 (z) 10246
7. 11.1 + 11.11 + 11.111 + 11.1111 Lkku Mkhðk¤ku fux÷kuÚkkÞ ?(y) 44.4012 (çk) 44.4321(f) 44.1111 (z) 44.1234
8. 44.7232323Lku .......... heíku ÷¾e þfkÞ.
(y) 44.7 23 (çk) 44.723
(f) 44.723 (z) 44.7239. Lke[uLkk yÃkqýkOfku Ãkife õÞk yÃkqýkofLke ®f{ík MkkiÚke LkkLke Au ?
(y) 83 (çk)
35 (f)
23 (z)
730
10. 20.80 + 20.008 + 20.088 + 20.888 = ?(y) 80.784 (çk) 81.784(f) 81.7845 (z) 80.7845
sðkçk :(1) f (2) y (3) y (4) f (5) f (6) z (7) çk (8) f (9) z (10) çk