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1 4 C) 9 1 4 D) −8 3 4 34. (97-3-9) Hisoblang. ³ 5 3 4 − 4 8 9 ´ · 2 + 67 1 2 : 2 1 7 A) 24 1 3 B) 33 2 9 C) 36 1 9 D) 31 1 3 35. (97-6-3) Hisoblang. ³ 5 9 − 1 1 6 · 1 2 ´ : 5 9 + 1 3 A) 3 20 B) 17 60 C) 7 30 D) − 7 60 36. (97-7-9) Hisoblang. ³ 4 1 10 − 3 4 15 ´ · 5 6 + 4 1 10 : 1 1 5 A) 3 5 9 B) 4 1 9 C) 5 2 3 D) 2 3 5 37. (97-10-9) Hisoblang. ³ 12 1 9 − 10 2 5 ´ : 38 1 2 + 2 8 9 · 18 A) 24 1 15 B) 32 7 45 C) 38 3 5 D) 52 2 45 38. (97-11-3) Hisoblang. ³ 3 17 36 − 5 7 12 ´ : 2 9 − 3 26 · 4 1 3 A) −9 B) 8 1 2 C) 9 D) −10 39. (07-107-1) Hisoblang. 8 3 4 + 5 12 : ³ 1 3 · 2 1 2 − 7 8 ´ A) −1 1 4 B) −6 3 4 C) −8 3 4 D) 9 1 4 17 1.2.3 O’nli kasrlar 1. Agar kasrning maxrajini 10 va uning dara- jalari ko’rinishida tasvirlash mumkin bo’lsa, bunday kasrga o’nli kasr deyiladai. 2. a · 10 −n = a 10 n ni o’nli kasrga aylantirish uchun a sonida chapdan o’ngga tomon n ta raqamdan so’ng vergul qo’yiladi. a da raqamlar soni n tadan kam bo’lsa, oldiga nol raqamlari qo’yiladi. Masalan, 2345 10 3 = 2, 345, 23 10 4 = 0, 0023. 1. (96-3-64) Hisoblang. 2, 701 · 10 −4 + 3, 205 · 10 −3 . A) 5, 906 · 10 −3 B) 5, 906 · 10 −4 C) 3, 4751 · 10 −3 D) 3, 0215 · 10 −4 Yechish: Umumiy ko’paytuvchi 10 −3 ni qavsdan tashqariga chiqaramiz. 2, 701·10 −4 +3, 205·10 −3 = 10 −3 (2, 701·10 −1 +3, 205) = 10 −3 (0, 2701 + 3, 205) = 3, 4751 · 10 −3 . Javob: 3, 4751 · 10 −3 (C). 2. (06-111-2) 2, 014 : 0, 19 + 2, 5 · 0, 3 ni hisoblang. A) 11, 35 B) 9, 35 C) 12, 85 D) 8, 85 3. (96-13-4) Ushbu 3, 104 · 10 −2 + 1, 81 · 10 −3 yig’indi quyidagi sonlarning qaysi biriga teng? A) 3, 285 · 10 −3 B) 3, 285 · 10 −2 C) 4, 914 · 10 −2 D) 4, 914 · 10 −3 4. (96-9-4) 1, 011 · 10 −3 + 2, 1 · 10 −4 ni hisoblang. A) 3, 111 · 10 −3 B) 3, 111 · 10 −4 C) 3, 111 · 10 −7 D) 1, 221 · 10 −3 5. (96-12-62) Hisoblang. 1, 015 · 10 −4 + 3, 14 · 10 −5 A) 4, 155 · 10 −4 B) 4, 155 · 10 −5 C) 4, 155 · 10 −9 D) 1, 329 · 10 −4 6. (98-12-8) Hisoblang. 3, 21 · 5, 95 − 4, 44 2, 21 · 5, 95 + 1, 51 A) 1 B) 2 C) 1 2 D) 1 1 2 Yechish: Kasr suratida quyidagicha almashtirish bajaramiz. 3, 21 · 5, 95 − 4, 44 = (2, 21 + 1) · 5, 95 − 4, 44 = = 2, 21 · 5, 95 + 5, 95 − 4, 44 = 2, 21 · 5, 95 + 1, 51 ekanidan 3, 21 · 5, 95 − 4, 44 2, 21 · 5, 95 + 1, 51 = 2, 21 · 5, 95 + 1, 51 2, 21 · 5, 95 + 1, 51 = 1 ni hosil qilamiz. Javob: 1 (A). 7. (98-7-9) Hisoblang. 2, 21 · 5, 95 + 1, 51 6, 42 · 5, 95 − 8, 88 A) 1 B) 1 2 C) 1 1 2 D) − 62 41 8. Hisoblang. 6, 86 · 4, 75 − 4, 62 2, 44 + 4, 75 · 2, 43 A) 1 B) 1 2 C) 2 D) −2 9. Hisoblang. 1, 27 · 3, 45 + 2, 25 4, 54 · 3, 45 − 2, 4 A) 1 B) 1 2 C) 1 1 2 D) − 1 2 10. (01-8-17) Hisoblang. 0, 21 : (0, 05 + 3 20 ) − 2, 5 · 1, 4 A) −2, 45 B) −2, 55 C) −2 D) −3, 35 Yechish: Dastlab qavs ichini hisoblaymiz. 0, 05 + 3 20 = 0, 05 + 15 100 = 0, 05 + 0, 15 = 0, 20. Ikkinchi, keyin birinchi tartibli amallarni bajarib 0, 21 : 0, 20 − 2, 5 · 1, 4 = 1, 05 − 3, 50 = −2, 45 ni olamiz. Javob: −2, 45 (A). 11. (01-2-11) Hisoblang. 4 − 3, 3 : ³ 2 1 7 − 1 1 5 ´ A) 3, 5 B) 2, 5 C) −1, 5 D) 0, 5 12. (00-5-17) Ifodaning qiymatini toping. −2, 4 + 3 1 3 − (−2, 6) A) −10, 6 B) 12, 5 C) 3 8 15 D) −12, 5 13. (00-5-18) Hisoblang. ³ − 3 8 ´ · (−32) + 0, 5 · (−8) A) 8 B) 4 C) 6 D) 7 14. (96-1-5) Hisoblang. ³ 2, 5 − 2 1 3 ´ · 5, 2 : 2 3 5 A) 2 3 B) 1 3 C) 3 D) 3 7 18 15. (96-6-1) Hisoblang. 1, 75 − ³ −1 2 7 ´ · 6, 5 · 7 9 A) −4, 75 B) 2, 15 C) 8, 25 D) 4, 75 16. (96-9-56) Hisoblang. 6 3 8 − ³ 2, 5 − 2 1 3 ´ : 1 1 3 A) 5 2 3 B) 6 1 4 C) 4 1 2 D) 2 1 3 Yechish: Dastlab qavs ichini hisoblaymiz: 2, 5 − 2 1 3 = 2 1 2 − 2 1 3 = (2 − 2) + 1 2 − 1 3 = 1 6 . 1 1 3 aralash kasrni noto’g’ri kasrga aylantirib, amal- larni bajaramiz 6 3 8 − 1 6 : 4 3 = 6 3 8 − 1 6 · 3 4 = 6 + 3 8 − 1 8 = 6 1 4 ni olamiz. Javob: 6 1 4 (B). 17. (97-1-7) Hisoblang. ³ 1 6 − 1 1 15 + 1 10 ´ : 0, 6 + 0, 4 A) 1 11 15 B) 0, 88 C) −1 1 3 D) − 14 15 18. (97-2-1) Hisoblang. −1 3 4 · 6, 5 · ³ − 4 7 ´ − 3, 75 A) −2, 75 B) −10, 25 C) 2, 75 D) 10, 25 19. (97-8-1) Hisoblang. 5, 8 − 3 7 · 2, 2 · ³ −2 1 3 ´ A) 3, 6 B) −8 C) 8 D) −3, 6 20. (97-11-7) Hisoblang. 0, 2 + 1, 8 · ³ 4 9 − 1 1 2 + 1 6 ´ A) −1, 4 B) 1, 8 C) 0, 04 D) −0, 36 21. (98-8-5) Hisoblang. 3 16 + 1 16 · (0, 312 : 0, 3 − 3, 15 · 1, 6) A) 1 4 B) 3 16 C) − 1 16 D) − 1 8 22. (98-1-3) Hisoblang. 19, 9 · 18 − 19, 9 · 16 + 30, 1 · 18 − 30, 1 · 16 A) 98 B) 100 C) 10 D) 110 Yechish: Birinchi va uchinchi qo’shiluvchilardan umumiy ko’paytuvchi 18 ni, ikkinchi va to’rtinchi qo’shiluvchilardan 16 ni qavsdan tashqariga chiqa- ramiz. Natijada 18(19, 9 + 30, 1) − 16(19, 9 + 30, 1) = 18·50−16·50 = 50(18−16) = 50·2 = 100. Javob: 100 (B). 23. (99-6-2) Hisoblang. 13, 5 · 5, 8 − 8, 3 · 4, 2 − 5, 8 · 8, 3 + 4, 2 · 13, 5 A) 42 B) 52 C) 50 D) 48 24. (00-2-1) Ifodaning qiymatini toping. 12, 7 · 64 + 173 · 3, 6 + 12, 7 · 36 + 17, 3 · 64 A) 3000 B) 1800 C) 2000 D) 3600 25. (98-8-3) Hisoblang. 109 · 9, 17 − 5, 37 · 72 − 37 · 9, 17 + 1, 2 · 72 A) 360 B) 350 C) 290 D) 380 26. (99-8-7) Ifodaning qiymatini toping. 79, 9 − 79, 8 + 79, 7 − 79, 6 + 79, 5 − 79, 4 + · · · + +60, 3 − 60, 2 + 60, 1 − 60 A) 100 B) 20 C) 10 D) 18, 8 27. (98-8-7) Hisoblang. ³ 5 6 · 5 − 5 ´ : 2 3 − 0, 5 2 A) 1 B) −1 C) 0, 5 D) −1, 5 Yechish: Dastlab qavs ichidagi amallarni ba- jaramiz. 5 6 · 5 − 5 = 25 6 − 5 = 25 − 30 6 = − 5 6 . Agar 0, 5 = 1 2 ekanligini hisobga olsak, 0, 5 2 = 1 4 ekanligini olamiz. Natijada, − 5 6 : 2 3 − 1 4 = − 5 6 · 3 2 − 1 4 = − 5 4 − 1 4 = − 6 4 = −1, 5. Javob: −1, 5 (D). 28. (98-1-7) Hisoblang. ( 2 3 : 3 − 1) · 1, 5 2 − 0, 25 A) 1, 5 B) −2 C) −5 D) −0, 2 29. (98-4-1) Hisoblang. (1, 6 2 − 2, 2 · 3 11 ) : 1, 4 A) 1, 4 B) 1, 2 C) 1, 5 D) 1, 6 30. (99-4-4) Hisoblang. 2, 8 · ³ 2 1 3 : 2, 8 − 1 ´ + 2 4 5 A) 5, 6 B) 2 2 3 C) 2 1 3 D) 2, 8 19 31. (00-6-2) Hisoblang. (0, 2 · 0, 1 − 0, 1) : 0, 25 + 0, 75 A) 1, 07 B) −2, 45 C) 3, 95 D) 0, 43 32. (00-6-3) Ifodaning qiymatini toping. (1 2 3 · 2, 2 + 1) : 2 1 5 − 5 11 A) 1 B) 1, 6 C) 2 1 3 D) 1 2 3 33. (07-109-1) Hisoblang. ³ 3, 5 − 3 1 3 ´ · 10, 4 : 5 1 5 A) 1 3 B) 2 5 C) 3 7 D) 1 12 34. (96-1-3) Ifodaning qiymatini toping. 6, 8 · 0, 04 · 1, 65 3, 3 · 5, 1 · 0, 16 A) 6 B) 1 2 C) 2 3 D) 1 6 Yechish: Kasr suratida verguldan keyingi raqam- lar sonini hisoblaymiz. Ular 5 ta. Endi kasr maxrajida verguldan keyingi raqamlar sonini hisob- laymiz. Ular 4 ta. Kasr maxrajidagi 5, 1 ni, unga teng bo’lgan 5, 10 bilan almashtiramiz, nati- jada kasr maxraji va suratida verguldan keyingi raqamlar soni tenglashadi. Kasr surati va maxra- jini 10 5 ga ko’paytiramiz 6, 8 · 0, 04 · 1, 65 · 10 5 3, 3 · 5, 10 · 0, 16 · 10 5 = 68 · 4 · 165 33 · 510 · 16 . Endi kasrni qisqatriramiz 68 · 4 · 165 33 · 510 · 16 = 17 · 4 · 4 · 33 · 5 33 · 17 · 30 · 16 = 5 30 = 1 6 . Javob: 1 6 (D). 35. (96-9-54) Ifodaning qiymatini toping. 0, 7 · 1, 8 · 2, 6 7, 2 · 7, 8 · 1, 4 A) 1 24 B) 2 5 C) 0, 04 D) 1 12 36. (96-10-3) Ifodaning qiymati nechaga teng? 0, 15 · 1, 6 · 4, 6 9, 2 · 0, 03 · 6, 4 A) 5 8 B) 2 5 C) 2 D) 0, 2 37. (99-4-3) Ifodaning qiymatini toping. 3, 2 · 0, 027 · 0, 005 0, 09 · 0, 0025 · 0, 64 A) 3 B) 0, 3 C) 30 D) 2 38. (03-5-1) Hisoblang. 0, 13 0, 00013 + 0, 02 0, 0005 − 0, 7 0, 0014 A) 540 B) 580 C) 620 D) 1400 39. (03-10-3) Ifodaning qiymatini toping. 0, 07 0, 21 + 0, 4 0, 06 + 0, 9 0, 05 A) 25 B) 20 C) 15 D) 30 40. (01-6-1) Hisoblang. 400 − 21, 5 · 18, 5 1, 5 · 2 1 5 + 2, 8 · 1 1 2 A) 2 7 B) 3 5 C) 3 7 D) 3 10 Yechish: Kasr suratini hisoblaymiz, 400 − 21, 5 · 18, 5 = 400 − 397, 75 = 2, 25. Endi kasr maxrajini 1, 5·2, 2+2, 8·1, 5 = 1, 5(2, 2+2, 8) = 1, 5·5 = 7, 5. Natijada, 2, 25 : 7, 5 = 0, 3 = 3 10 . Javob: 3 10 (D). 41. (96-10-5) Hisoblang. (5 1 3 − 3, 2) : 2 2 3 + 1 2 5 A) 2 1 2 B) 2, 2 C) 3, 2 D) 2 42. (98-6-4) Hisoblang. [(1, 2 : 36) + 0, 3] · 9 0, 2 A) 148, 5 B) 1, 5 C) 150 D) 15 43. (01-5-1) Hisoblang. (6 3 5 − 3 3 14 ) · 5 5 6 (21 − 1, 25) : 2, 5 A) 2, 5 B) 3 C) −2, 5 D) 4 44. (99-2-1) Hisoblang. 7, 4 + 13 17 · 0, 15 · 1 4 13 · 6 2 3 0, 2 · 5 − 0, 16 A) 10 B) 8 C) 12 D) 6 45. (00-1-1) Hisoblang. 5 11 · 0, 006 · 2 1 5 + 1 1 8 · 0, 004 · 8 9 0, 5 · 0, 0009 + 0, 0001 · 0, 5 A) 10 B) 0, 4 C) 20 D) 2 46. (02-4-1) Hisoblang. ³ 2 3 4 − 0, 25 ´ · 0, 8 − 1 2 3 · 1, 8 A) 1 B) 1, 5 C) −1 D) −1, 5 47. (02-6-1) Hisoblang. 32 · 0, 99 · 25 · 1, 25 + 411 + 57 · 5 · 0, 4 · 25 · 4 19 A) 2001 B) 2000 C) 1999 D) 2002 20 1.2.4 Cheksiz davriy o’nli kasrlar Cheksiz o’nli kasrlarning kasr qismidagi bir yoki bir necha raqamlari bir xil tartibda ketma-ket takrorlansa, bunday kasrlar cheksiz davriy o’nli kasrlar deb, takror- lanadigan raqamlar gruppasiga shu kasrning davri deb ataladi. Davr qavsga olib yoziladi. Masalan, 0, 5555 . . . = 0, (5); 2, 1232323 . . . = 2, 1(23). Cheksiz davriy o’nli kasr ko’rinishida tasvirlash mumkin bo’lgan sonlar rat- sional sonlar deyiladi. 1. Agar qisqarmas kasrning maxrajini tub ko’- paytuvchilarga ajratganda 2 va 5 sonlari- dan boshqa tub ko’paytuvchilar uchrasa, bunday kasr cheksiz davriy o’nli kasr bo’ladi. Misollar: 3 48 = 1 16 = 1 2 4 - chekli o’nli kasr. 5 12 = 5 2 2 3 - cheksiz davriy o’nli kasr. 2. Davriy kasrlar ikki xil bo’ladi. a) agar davr verguldan keyin darhol boshlansa, bunday davriy kasr sof davriy kasr deyiladi. Misol: 0, 333 . . . = 0, (3), 2, 161616 . . . = 2, (16). b) agar davr verguldan keyin darhol bosh- lanmasa, bunday davriy kasr aralash davriy kasr deyiladi. Misol: 0, 377 . . . = 0, 3(7), 2, 81212 . . . = 2, 8(12) 3. Sof davriy kasr shunday oddiy kasrga tengki, uning maxraji davrda nechta raqam bo’lsa shuncha 9 dan, surati esa davrning o’zidan iborat. Masalan, 0, (3) = 3 9 = 1 3 , 2, (16) = 2 16 99 . 4. Aralash davriy kasr shunday oddiy kasrga tengki, uning maxraji davrda nechta raqam bo’lsa shuncha 9 va verguldan keyin davr- gacha nechta raqam bo’lsa shuncha 0 dan tuzilgan sondan, surati esa verguldan keyingi ikkinchi davrgacha bo’lgan raqamlardan tuzil- gan sondan birinchi davrgacha bo’lgan raqam- lardan tuzilgan son ayirmasidan iborat. Masalan, 0, 3(7) = 37 − 3 90 = 34 90 = 17 45 , 2, 8(12) = 2 812 − 8 990 = 2 804 990 = 2 134 165 . 1. (96-1-12) Quyidagi sonlardan qaysi biri 0, (2) ga teng? A) 1 9 B) 2 9 C) 2 3 D) 0, 22 Yechish: 0, (2) sof davriy kasr, 3-qoidaga ko’ra 0, (2) = 2 9 dir. Javob: 2 9 (B). 2. (96-9-62) Quyidagi sonlardan qaysi biri 0, (5) ga teng? A) 1 2 B) 5 9 C) 0, 555 D) 1 5 3. (97-9-71) 8, (5) ni oddiy kasrga aylantiring. A) 8 4 9 B) 8 5 8 C) 8 7 8 D) 8 5 9 4. 0, (18) ni oddiy kasr shaklida yozing. A) 2 11 B) 18 90 C) 8 99 D) 18 900 5. (99-4-27) 0, 5(6) soni quyidagilardan qaysi biriga teng? A) 56 99 B) 1 18 C) 17 30 D) 28 45 6. (01-6-22) 0, 2(3) ni oddiy kasrga aylantiring. A) 7 30 B) 4 15 C) 3 8 D) 2 7 7. (03-8-27) 0, 2(18) ni oddiy kasr shaklida yozing. A) 12 55 B) 13 55 C) 28 99 D) 218 900 8. (02-11-2) 3 127 495 ni cheksiz davriy o’nli kasr ko’ri- nishida yozing. A) 3, (127) B) 3, (254) C) 3, 2(54) D) 3, 2(56) 9. (99-7-6) Hisoblang. 0, (5) + 0, (1) A) 2 3 B) 1 3 C) 1, 5 D) 1 4 Yechish: 0, (5) va 0, (1) sof davriy kasrlardir. Ularni 3-qoidaga ko’ra oddiy kasrlarga aylanti- ramiz. 0, (5) = 5 9 ; 0, (1) = 1 9 . Endi ularni qo’sha- miz. 5 9 + 1 9 = 6 9 = 2 3 . Javob: 2 3 (A). 10. (98-5-4) 0, (8) + 0, (7) ni hisoblang. A) 0, (15) B) 1, (6) C) 1, (5) D) 1, (15) 11. (01-3-39) 0, (8) + 0, (3) ni hisoblang. A) 1 1 9 B) 1 2 9 C) 1, (11) D) 1, (1) 12. (02-5-2) 0, 5(6) + 0, (8) ni hisoblang. A) 0, 6(4) B) 1, 3(6) C) 1 Download 1.09 Mb. Do'stlaringiz bilan baham: |
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