{"id":6494,"date":"2021-03-09T12:14:42","date_gmt":"2021-03-09T06:44:42","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=6494"},"modified":"2021-09-15T11:39:26","modified_gmt":"2021-09-15T06:09:26","slug":"ap-board-8th-class-maths-solutions-chapter-4-ex-4-2","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-8th-class-maths-solutions-chapter-4-ex-4-2\/","title":{"rendered":"AP Board 8th Class Maths Solutions Chapter 4 Exponents and Powers Ex 4.2"},"content":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions<\/a> Chapter 4 Exponents and Powers Ex 4.2 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 8th Class Maths Solutions 4th Lesson Exponents and Powers Exercise 4.2<\/h2>\n

\"AP<\/p>\n

Question 1.
\nExpress the following numbers in the standard form.
\n(i) 0.000000000947
\nSolution:
\n= \\(\\frac{947}{1000000000000}\\) = 947 \u00d7 10-12<\/sup><\/p>\n

(ii) 543000000000
\nSolution:
\n= 543 \u00d7 1000000000 = 543 \u00d7 109<\/sup><\/p>\n

(iii) 48300000
\nSolution:
\n= 483 \u00d7 100000 = 483 \u00d7 105<\/sup><\/p>\n

\"AP<\/p>\n

(iv) 0.00009298
\nSolution:
\n= \\(\\frac{9298}{100000000}\\)
\n= 9298 \u00d7 10-8<\/sup><\/p>\n

(v) 0.0000529
\nSolution:
\n= \\(\\frac{529}{10000000}\\)
\n= 529 \u00d7 10-7<\/sup><\/p>\n

Question 2.
\nExpress the following numbers in the usual form.
\n(i) 4.37 \u00d7 105<\/sup>
\nSolution:
\n= 4.37 \u00d7 100000
\n= 437000<\/p>\n

(ii) 5.8 \u00d7 107<\/sup>
\nSolution:
\n= 5.8 \u00d7 10000000<\/p>\n

(iii) 32.5 \u00d7 10-4<\/sup>
\nSolution:
\n= \\(\\frac{32.5}{10^{4}}=\\frac{32.5}{10000}\\)
\n= 0.00325<\/p>\n

\"AP<\/p>\n

(iv) 3.71529 \u00d7 107<\/sup>
\nSolution:
\n= 3.71529 \u00d7 10000000
\n= 37152900<\/p>\n

(v) 3789 \u00d7 10-5<\/sup>
\nSolution:
\n= \\(\\frac{3789}{10^{5}}=\\frac{3789}{100000}\\)
\n= 0.03789<\/p>\n

(vi) 24.36 \u00d7 10-3<\/sup>
\nSolution:
\n= \\(\\frac{24.36}{10^{3}}=\\frac{24.36}{1000}\\)
\n= 0.02436<\/p>\n

Question 3.
\nExpress the following information in the standard form
\n(i) Size of the bacteria is 0.0000004 m
\nSolution:
\n= [klatex]\\frac{4}{10000000}[\/latex] m = 4 x 10-7<\/sup> m<\/p>\n

(ii) The size of red blood cells is 0.000007mm
\nSolution:
\n= \\(\\frac{7}{1000000}\\) = 7 \u00d7 10-6<\/sup><\/p>\n

\"AP<\/p>\n

(iii) The speed of light is 300000000 m\/sec
\nSolution:
\n= 3 \u00d7 10,00,00,000 = 3 \u00d7 108<\/sup> m\/sec<\/p>\n

(iv) The distance between the moon and the earth is 384467000 m(app)
\nSolution:
\n= 384467 \u00d7 1000 m
\n= 384467 \u00d7 103<\/sup><\/p>\n

(v) The charge of an electron is 0.0000000000000000016 coulombs
\nSolution:
\n= 0.0000000000000000016
\n= \\(\\frac{16}{10000000000000000000}\\)
\n= \\(\\frac{16}{10^{19}}\\)
\n= 16 \u00d7 10-19<\/sup> coulombs<\/p>\n

(vi) Thickness of a piece of paper is 0.0016 cm
\nSolution:
\n= 0.0016 cm = \\(\\frac{16}{10000}\\)
\n= \\(\\frac{16}{10^{4}}\\)
\n= 16 \u00d7 10-4<\/sup> cm<\/p>\n

(vii) The diameter of a wire on a computer chip is 0.000005 cm
\nSolution:
\n= 0.000005 cm = \\(\\frac{5}{1000000}\\) cm
\n= \\(\\frac{5}{10^{6}}\\) cm = 5 \u00d7 10-6<\/sup> cm<\/p>\n

\"AP<\/p>\n

Question 4.
\nIn a stack, there are 5 books, each of thickness 20 mm and 5 paper sheets each of thickness 0.016mm. What is the total thickness of the stack.
\nSolution:
\nThe thickness of 5 books of a pack
\n= (5 books \u00d7 their thickness)
\n= 5(papers \u00d7 their thickness)
\n= (20 mm \u00d7 5) + (0.016 mm \u00d7 5)
\n= 100 mm + 0.080 mm
\n= (100 + 0.080) mm
\n= 100.08 mm
\n= 1.0008 \u00d7 102<\/sup> mm<\/p>\n

Question 5.
\nRakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
\n(i) x-3<\/sup> \u00d7 x-2<\/sup> = x-6<\/sup>
\nSolution:
\nx-3<\/sup> \u00d7 x-2<\/sup> = x-6<\/sup>
\n= x-3+(-2)<\/sup> = x-6<\/sup> [\u2235 am<\/sup> \u00d7 an<\/sup> = am + n<\/sup> ]
\n= x-5<\/sup> = x-6<\/sup>
\n= -5 = -6(False)
\n\u2234 In this case do not agree with Rakesh solution.<\/p>\n

\"AP<\/p>\n

(ii) \\(\\frac{X^{3}}{X^{2}}\\) = x4<\/sup>
\nSolution:
\n\u21d2 x3-2<\/sup> = x4<\/sup> [\u2235 \\(\\frac{a^{m}}{a^{n}}\\) = am – n<\/sup> ]
\n\u21d2 x1<\/sup> = x4<\/sup>
\n[\u2235Here bases are equal, so exponents are also equal]
\n\u21d2 1 = 4 (It is false)
\n\u2234 I do not agree with Rakesh solution.<\/p>\n

(iii) (x2<\/sup>)3<\/sup> = (x2<\/sup>)3<\/sup> = x8<\/sup>
\nSolution:
\n(x2<\/sup>)3<\/sup> = \\(x^{2^{3}}\\) = x8<\/sup>
\n\u21d2 (x2<\/sup>)3<\/sup> = \\(x^{2^{3}}\\)
\n\u21d2 x2 \u00d7 3<\/sup> = \\(x^{2^{3}}\\)
\n\u21d2 x6<\/sup> = x2 \u00d7 2 \u00d7 2<\/sup>
\n\u21d2 x6<\/sup> = x8<\/sup>
\n[\u2235 Bases are equal, so exponents are also equal]
\n\u21d2 6 = 8
\nIt is false
\n\u2234 Rakesh solution is wrong.<\/p>\n

(iv) x-2<\/sup> = \u221ax
\nSolution:
\n\u21d2 x-2<\/sup> = x1\/2<\/sup>
\n\u21d2 -2 = 1\/2 (it is false)
\n\u2234 I don\u2019t agree with Rakesh solution.<\/p>\n

\"AP<\/p>\n

(v) 3x-1<\/sup> = \\(\\frac{1}{3 x}\\)
\nSolution:
\n\u21d2 3x-1<\/sup> = \\(\\frac{1}{3 x}\\)
\n\u21d2 3 \u00d7 3 = \\(\\frac{x}{x}\\)
\n\u21d2 x0<\/sup> = 9
\n\u21d2 1 = 9
\nIt is false
\n\u2234 I don\u2019t agree with Rakesh solution.<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 4 Exponents and Powers Ex 4.2 Textbook Questions and Answers. AP State Syllabus 8th Class Maths Solutions 4th Lesson Exponents and Powers Exercise 4.2 Question 1. Express the following numbers in the standard form. (i) 0.000000000947 Solution: = = 947 \u00d7 10-12 (ii) 543000000000 Solution: …<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/6494"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=6494"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/6494\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=6494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=6494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=6494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}