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？,