標題:
Math questions
發問:
1. Convert the following decimals into fractions. Leave your answers in the simplest form. (a) 0.17(0.177777777.....) (b) 0.17(0.17171717......) 2. Determine whether each of the following numbers is rational or irrational. (a)4.12(4.12121212......) - 3.6(3.66666666......) (b)√2√8 (c) (1 + √3)(1 - √3) 更新: MUST SHOW THE STEPS CLEARLY. 更新 2: I forcus on this question. You need to show the steps to show that your determination is correct or not. Determine whether each of the following numbers is rational or irrational. 2(a)4.12(4.12121212......) - 3.6(3.66666666......)
最佳解答:
1(a) Let a = 0.1777.... 10a = 1.777... 100a = 17.777.... 100a-10a = 17.777...-1.777... = 16 therefore, 90a = 16 a = 16/90 0.17=17/100 0.17(0.177777777.....) = 17/100(16/90) = 34/1125 (b) Let b = 0.1717... 100b = 17.1717... 100b-b = 17.1717...-0.1717 = 17 b = 17/99 0.17(0.17171717......) = 17/100(17/99) = 289/9900 2. (a)It is rational since you can convent 4.12(4.12121212......) and 3.6(3.66666666......) to fractions by using the above method. i.e. 4.12 = 412/100 4.1212.... = (412-4)/99 = 408/99 =136/33 3.6 = 36/10 3.666... = (36-3)/9 = 33/9 = 11/3 (412/100)(136/33) - (36/10)(11/3) = 3118/825 thus it is RATIONAL (b)√2√8 = √16 = 4 thus it is RATIONAL (c) (1 + √3)(1 - √3) = 1 - 3 = -2 thus it is RATIONAL
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