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【329574】2.6 实数 同步巩固

时间:2025-02-02 18:24:39 作者: 字数:3016字


 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a>

2.6 实数

1.下列各数中:

 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a>3.14159,π, <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> , <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,0,0. <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> , <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> , <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,2.121122111222…

其中有理数有________________ _______.

无理数有____________________________.

2.判断正误

1)有理数包括整数、分数( )

2)无理数都是开方开不尽的数( )

3)不带根号的数都是有理数( )

4)带根号的数都是无理数( )

5)无理数都是无限小数( )

6)无限小数都是无理数( )

3.由于水资源缺乏,BC两地不得不从黄河上的扬水站A处引水,这就需要在ABC之间铺设地下管道.有人设计了三种方案:如图甲,图中实线表示管道铺设线路,在图乙中,ADBCD,在图丙中,OA=OB=OC,为减少渗漏、节约水资源,并降低工程造价,铺设线路尽量缩短.已知△ABC是一个边长为a的等边三角形,请你通过计算,判断哪个铺设方案好?

 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a>











4. 几百年前的某一天,数字王国的国王召集他的臣民们开会.整数、分数等大批臣民纷纷到场,一时间会场里你推我挤,熙熙嚷嚷,吵个不休.国王非常生气,就想了一个办法,让他们排排站,他画了一条直线,指定直线上的某点O为数零的位置,叫原点,并且规定向右的方向为正方向,负整数和正整数分别站在原点左右两侧指定的位置上,正分数和负分数在数O的指挥下也找到了自己的位置,这时± <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ± <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ……,还有π等无理数不干了:“国王,我们站在哪里呢?”“别着急,直线上有你们的位置”.于是国王亲自动手找到了他们各自的位置.这时这条直线排满了有理数、无理数,国王下令:“这条直线就叫做数轴吧.”

1)请你画一条数轴.

2在你所画的数轴上,你能找出 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> 的位置吗?怎样找到的?

3)- <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,- <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,- <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> 的位置呢?

4)通过阅读以上材料和解题,你明白了什么?


参考答案

1.有理数:- <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a>3.14159,0,0.3, <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> , <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a>

无理数有: <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,π, <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> , <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,2.12112111222……

2.(1)√ (2)× (3)× (4)× (5)√ (6)×

3.解:对于甲:AB+AC=a+a=2a

对于乙:∵△ABC为等边三角形

BD=DC= <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> BC= <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> a

Rt△ADB中,AD= <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> = <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> a

AD+BC= <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> a+a=( <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> +1)a

对于丙:OA=OB=OC= <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> × <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> a= <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> a

OA+OB+OC= <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> a

∵2 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> , <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a>  <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,∴ <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> 1

 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> +1 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> + <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> = <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a>

∴2 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> +1 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a>

2a( <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> +1)a <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> a

图丙的铺设方案好.

4.1)如图

 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a>

2)以单位1为直角边作一等腰直角三角形OAB,则OB= <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,以OB为一直角边,B为直角顶点,1为另一直角边再建直角三角形,则斜边为 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> . <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> 为直角边再建立直角三角形,则斜边上即为 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,这样 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,线段的长度就确定了.O为圆心, <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> 分别为半径画弧交于原点右方的点,即为 <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> 对应的点.

3)交于原点左方的点即为- <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,- <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> ,- <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/90/" title="巩固" class="c1" target="_blank">巩固</a> <a href="/tags/842/" title="实数" class="c1" target="_blank">实数</a> 所对应的点.

4)有理数和无理数都可以用数轴上的点来表示.