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实 数,知识回顾,1、无理数:,无限不循环小数叫做无理数,2、有理数:,有限和无限循环小数属于有理数,或整数与分数统称为有理数,(1)到目前为止,你认识了哪些数?,自然数,分数,负数,有理数,小数,负整数,正整数,零,有限小数,无限不循环小数-无理数,负有理数,想一想,无限不循环小数,(2)你会把实数加以分类吗?你所确定的分类标准是什么?按你确定的标准进行一次分类后,还能再确定另一个指标作为标准,把其中的每一类再进一步分类吗?,有限小数或无限循环小数,按性质分类,实数,按大小分类,有一定的规律,但不循环的无限小数都是无理数。,0.1010010001两个1之间依次多1个0,234.232232223两个3之间依次多1个2,0.12345678910111213 小数部分有相继的正整数组成,例如,像 的数是无理数。,圆周率 及一些含有 的数都是无理数,思考:,一个无理数的相反数与绝对值分别是什么数?,例1 下列各数哪些是有理数?哪些是无理数?哪些是正数?哪些是负数?,-8,8,0.27,0,-5.151 151 115(相邻两个5之间一次多1个1),0.101001,22/7,- 3/3,5.15.,3,.,解:有理数: -8, 0.27,0.101001, 22/7, 5.15;,3,.,无理数: 8, , -5.151 151 115 - 3/3;,正数: 8, , 0.27, 0.101001, 22/7, 5.15;,.,负数: -8, -5.151 151 115 - 3/3.,3,练习 将下列各数放入图中适当的位置:,-0.101001000100001、,、 4、 3.14、,0.373373337,4,0、,-2,-0.101001000100001、,3.14、,0.373373337,(它的位数无限且相邻的两个 3之间7的个数依次加1),0、,-2、,练习 判断下列说法是否正确:,议一议,1,A,B,如图:OA=OB,数轴上A点对应的数是什么?,如果将所有有理数都标到数轴上,那么数轴被填满了吗?,1、每个实数都可以用数轴上的一个点来表示;反过来,数轴上的每一个点都表示一个实数.即实数和数轴上点是一一对应的.,2、同样,在数轴上,右边的点表示的数比左边的点表示的数大.,总结:,4、有序实数对与坐标平面上的点也是一一对应的。,3、如果a是实数,那么a就是在数轴上表示数a的点,到原点的距离。,在实数范围内,相反数、倒数、绝对值的意义和有理数范围内的相反数、倒数、绝对值的意义完全一样。,在数轴上作出 的对应点.,0,1,2,3,-1,1,2,0,1,2,-1,-2,A,一个实数a,-1,-1,0,-1,1,0,-1,1,0,-1,3,1,0,-1,3,1,0,-1,3,3,1,3,0,1,3,-1,0,1,3,1、每个实数都可以用数轴上的一个点来表示;反过来,数轴上的每一个点都表示一个实数.即实数和数轴上点是一一对应的.,2、同样,在数轴上,右边的点表示的数比左边的点表示的数大.,数轴上一个点,有一个实数,有一个实数,数轴上一个点,例如:,例2 比较下列各组数中两个数的大小:,(1)3.14与; (2)-3与-3.,3,解:(1)3.141,3.14.,(2) -3 -1.732, -3 -1.442 -3 -3,3,3,shop.99114.com/50657958 shop.99114.com/50498383 shop.99114.com/47774270 shop.99114.com/50607661 shop.99114.com/50657309 shop.99114.com/50662497 shop.99114.com/47859702 shop.99114.com/50521841 shop.99114.com/49151641 shop.99114.com/50648237 shop.99114.com/50640413 shop.99114.com/50532750 shop.99114.com/43562073 shop.99114.com/50632314 shop.99114.com/50299211 shop.99114.com/49764738 shop.99114.com/50646709 shop.99114.com/50608292 shop.99114.com/50642730 shop.99114.com/50662546 shop.99114.com/50663613 shop.99114.com/49783030 shop.99114.com/50631631 shop.99114.com/47773595 shop.99114.com/49827561 shop.99114.com/50674736 shop.99114.com/49766140 shop.99114.com/47849249 shop.99114.com/50669560 shop.99114.com/50658420 shop.99114.com/50659587 shop.99114.com/50510133 shop.99114.com/50629770 shop.99114.com/50656890 shop.99114.com/41498558 shop.99114.com/49824056 shop.99114.com/47864808 shop.99114.com/45414995 shop.99114.com/49687733 shop.99114.com/50672978 shop.99114.com/50673083 shop.99114.com/47878067 shop.99114.com/50649987 shop.99114.com/50617012 shop.99114.com/50665145 shop.99114.com/50647123 shop.99114.com/50292167 shop.99114.com/50655190 shop.99114.com/50627787 shop.99114.com/50659871 shop.99114.com/50513305 shop.99114.com/50662881 shop.99114.com/50665133 shop.99114.com/50653799 shop.99114.com/50659034 shop.99114.com/50666877 shop.99114.com/50654456 shop.99114.com/50656905 shop.99114.com/50823560 shop.99114.com/50658603 shop.99114.com/50664977 shop.99114.com/50489520 shop.99114.com/50294049 shop.99114.com/50508111 shop.99114.com/50578361 shop.99114.com/50661888 shop.99114.com/50637656 shop.99114.com/50670631 shop.99114.com/50497599 shop.99114.com/50626129 shop.99114.com/50665651 shop.99114.com/50662632 shop.99114.com/50477386 shop.99114.com/42298014 shop.99114.com/50523857 shop.99114.com/50664627 shop.99114.com/50672524 shop.99114.com/50667797 shop.99114.com/50601952 shop.99114.com/50628845 shop.99114.com/50639356 shop.99114.com/50672506 shop.99114.com/50639813 shop.99114.com/50587461 shop.99114.com/50532719 shop.99114.com/50657075 shop.99114.com/50659646 shop.99114.com/50674761 shop.99114.com/50801644 shop.99114.com/50648576 shop.99114.com/49705090 shop.99114.com/50658375 shop.99114.com/50658371 shop.99114.com/50655033 shop.99114.com/50812991 shop.99114.com/50665062 shop.99114.com/50512368 shop.99114.com/50672963 shop.99114.com/50578366 shop.99114.com/50813319,例3 求下列各数的相反数和绝对值:,(1)2-3; (2) 5-6.,解:(1)2-3的相反数是-( 2-3 )=-2+3 30, |2-3|=2-3.,(2) 5-6的相反数是-( 5-6 )=- 5+6= 6-5 56, 5-60, |5-6|= 6-5.,练习:求下列各数的相反数、倒数和绝对值:,2,2,-7,7,1、a、b互为相反数,c与d互为倒数则a+1+b+cd=。,2、实数a,b,c,d在数轴上的对应点如图11所示,则 它们从小到大的顺序是 。,其中:,2,cdba,a+b,-d-c,b-c,a-d,练习:,总结与回顾,这节课你有什么收获?,你对本节课的内容还有哪些疑问?,
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