[从头学数学] 第54节 小数的初步认识

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入练气期第六层功法的修炼，
这次要修炼的目标是[小数的初步认识]。

正剧开始：

星历2016年01月21日 12:02:18, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起学习[小数]。

小伟说：这多了一个小数点，数字应该怎样读呢？

阿伟于是给小伟又做了一个读小数的工具，来看看效果吧：

<span style="font-size:18px;">###
# @usage   小数的读法
# @author  mw
# @date    2016年01月21日  星期四  09:53:40 
# @param
# @return
#
###
def floatNumberRead(num):
    #正负号
    if (num < 0):
        sign = '负';
    else:
        sign = '';

    #判断是否小数 
    sOfNum = str(num);
    index = sOfNum.find('.');
    if (index != -1):
        chineseOfNumber=['零','一', '二', '三', '四', '五', '六',\
                     '七', '八', '九'];
        sOfNum = sOfNum[index+1:];
        decimalPart = '点';
        for i in range(len(sOfNum)):
            decimalPart += chineseOfNumber[int(sOfNum[i])];
            
        import math;
        intPart = numberToChinese(math.floor(abs(num)), '');

        return sign+intPart+decimalPart;
    else:
        return sign+numberToChinese(num, '');        </span>

<span style="font-size:18px;">if __name__ == '__main__':
    a = [3.45, 0.85,2.60,36.6,1.2,1.5];
    for i in range(len(a)):
        print(floatNumberRead(a[i]));

>>> 
三点四五
零点八五
二点六
三十六点六
一点二
一点五</span>

小伟很高兴，现在他会读小数了。

阿伟说：当然，上面的工具要依赖下面这个工具：

<span style="font-size:18px;">###
# @usage   数字的中文写法 
# @author  mw
# @date    2016年01月08日  星期五  12:37:26 
# @param
# @return
#
###
def numberToChinese(num, s):
    if (num < 0):
        num = abs(num);
    chineseOfNumber=['零','一', '二', '三', '四', '五', '六',\
                     '七', '八', '九', '十','百','千','万','亿'];
    bit = 0;
    tmp = num;
    if (tmp == 0):
        s = chineseOfNumber[0];
    while (tmp > 0):
        tmp = tmp//10;
        bit+=1;
    tmp = num;
    while (tmp > 0):
        if (tmp < 10):
            s += chineseOfNumber[tmp];
            tmp -= 10;
        elif (tmp < 100):
            s += chineseOfNumber[tmp//10];
            s += '十';
            tmp = tmp%10; 
        elif (tmp < 1000):
            s += chineseOfNumber[tmp//100];
            s += '百';
            tmp = tmp%100;
            if tmp < 10 and tmp > 0:
                s += '零';
        elif (tmp < 10000):
            s += chineseOfNumber[tmp//1000];
            s += '千';
            tmp = tmp%1000;
            if tmp < 100 and tmp > 0:
                s += '零';
        elif (tmp < 100000000):
            s1 = '';
            s += numberToChinese(tmp//10000, s1);
            s += '万';
            tmp =tmp%10000;
            if tmp < 1000 and tmp > 0:
                s += '零';
        elif (tmp >= 100000000):
            s1 = '';
            s += numberToChinese(tmp//100000000, s1);
            s += '亿';
            tmp = tmp%100000000;
            if tmp < 10000000 and tmp > 0:
                s += '零';
        else:
            pass;
    return s;</span>

小伟拿到了新工具，当然要好好地去试用了：

<span style="font-size:18px;">>>> 
三点五
五点二五
二点七五
一点五
五点八

if __name__ == '__main__':
    a = [3.5,5.25,2.75,1.5,5.8];
    for i in range(len(a)):
        print(floatNumberRead(a[i]));</span>

接着，小伟又看到了这个题：

小伟知道，这种题的答案会很多，到底有多少呢，阿伟和小伟都很好奇。

<span style="font-size:18px;">>>> 
大于1的两位小数有[50.76, 50.67, 57.06, 56.07, 5.76, 5.67, 7.56, 7.65, 6.57, 6.75, 75.06, 70.56, 70.65, 76.05, 65.07, 60.57, 60.75, 67.05], 共计18个。
大于7的两位小数有[50.76, 50.67, 57.06, 56.07, 7.56, 7.65, 75.06, 70.56, 70.65, 76.05, 65.07, 60.57, 60.75, 67.05], 共计14个。

#全排列
def perm(array):
    if (len(array)<=1):
        return [array];

    r = [];
    for i in range(len(array)):
        #抽去array[i]
        s = array[:i]+array[i+1:];
        p = perm(s);
        for x in p:
            #array[i]置顶
            r.append(array[i:i+1]+x);
    return r;

def tmp():
    a = [5, 0, 7, 6];

    #选择集
    b = perm(a);
    #结果集
    result = [];
    result2 = [];

    import math;
    for i in range(len(b)):
        sum = round(b[i][0] * 10 + b[i][1] * 1 +\
                         b[i][2] * 0.1 + b[i][3] * 0.01, 2);
        if sum > 1 and b[i][3] != 0:
            result.append(sum);

        if sum > 7 and b[i][3] != 0:
            result2.append(sum);

    print('大于1的两位小数有{0}, 共计{1}个。'.format(result, len(result)));
    print('大于7的两位小数有{0}, 共计{1}个。'.format(result2, len(result2)));</span>

原来如此，阿伟和小伟都满足了好奇心。

又到了要计算四则运算的时候了，多了小数点，原来的竖式工具又不好用了，于是，阿伟又做了改进。

增加小数的加法竖式：

<span style="font-size:18px;">/**
* @usage   小数加法竖式
* @author  mw
* @date    2016年01月21日  星期四  10:49:56 
* @param
* @return
*
*/
	this.floatAdd = function(augend, addend, precision, x, y, r) {
		
		var decimalPointPos = -1;
		
		plot.save()
			.setFillStyle('black');
			
		var result = addend + augend;
		var xBeg = x ? x : 300, yBeg = y ? y :100, r = r ? r : 20;		
		var maxBit = Math.max(addend, augend).toFixed(0).length;
		var decimalString = '';
		
		//整数和小数部分的分解
		augendDecimalPart = augend > 0 ? augend - Math.floor(augend) : Math.ceil(augend)- augend;		
		addendDecimalPart = addend > 0 ? addend - Math.floor(addend) : Math.ceil(addend)-addend;
		resultDecimalPart = result > 0 ? result - Math.floor(result) : Math.ceil(result)-result;
		
		augend = augend > 0 ? Math.floor(augend) : Math.ceil(augend);		
		addend = addend > 0 ? Math.floor(addend) : Math.ceil(addend);
		result = result > 0 ? Math.floor(result) : Math.ceil(result);		
		
		
		x = xBeg, y = yBeg + r;
		var plusPos = x - (maxBit+2) * r;
		this.rightAlign(augend, x, y, r);
		
		decimalString = augendDecimalPart.toFixed(precision);
		decimalPointPos = decimalString.indexOf('.');
		if (decimalPointPos != -1) {
			decimalString = decimalString.substr(decimalPointPos+1, precision);
			augendDecimalPart = parseInt(decimalString);
			plot.fillText('.', x, y+0.4*r, r);
			this.leftAlign(augendDecimalPart, x + r, y , r);
		}
		
		y += 1.5 * r;
		this.rightAlign(addend, x, y, r);
		
		decimalString = addendDecimalPart.toFixed(precision);
		decimalPointPos = decimalString.indexOf('.');
		if (decimalPointPos != -1) {
			decimalString = decimalString.substr(decimalPointPos+1, precision);
			addendDecimalPart = parseInt(decimalString);
			plot.fillText('.', x, y+0.4*r, r);
			this.leftAlign(addendDecimalPart, x + r, y , r);
		}
			
		plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial')
			.fillText('+', plusPos, y+0.4*r, r);
		
		y += r;
		plot.beginPath()
			.moveTo(plusPos - r, y)
			.lineTo(x + (precision+ 2) *r, y)
			.closePath()
			.stroke();
			
		y += r;
		this.rightAlign(result, x, y, r);
		
		decimalString = resultDecimalPart.toFixed(precision);
		decimalPointPos = decimalString.indexOf('.');
		if (decimalPointPos != -1) {
			decimalString = decimalString.substr(decimalPointPos+1, precision);
			resultDecimalPart = parseInt(decimalString);
			plot.fillText('.', x, y+0.4*r, r);
			this.leftAlign(resultDecimalPart, x + r, y , r);
		}
			
			
		plot.restore();
	}
</span>

增加小数的减法竖式：

<span style="font-size:18px;">/**
* @usage   小数减法竖式
* @author  mw
* @date    2016年01月21日  星期四  10:49:56 
* @param
* @return
*
*/
	this.floatSub = function(minuend, subtrahend, precision, x, y, r) {
		
		var decimalPointPos = -1;
		
		plot.save()
			.setFillStyle('black');
			
		var result = minuend -subtrahend ;
		var xBeg = x ? x : 300, yBeg = y ? y :100, r = r ? r : 20;		
		var maxBit = Math.max(subtrahend, minuend).toFixed(0).length;
		var decimalString = '';
		
		//整数和小数部分的分解
		minuendDecimalPart = minuend > 0 ? minuend - Math.floor(minuend) : Math.ceil(minuend)- minuend;		
		subtrahendDecimalPart = subtrahend > 0 ? subtrahend - Math.floor(subtrahend) : Math.ceil(subtrahend)-subtrahend;
		resultDecimalPart = result > 0 ? result - Math.floor(result) : Math.ceil(result)-result;
		
		minuend = minuend > 0 ? Math.floor(minuend) : Math.ceil(minuend);		
		subtrahend = subtrahend > 0 ? Math.floor(subtrahend) : Math.ceil(subtrahend);
		result = result > 0 ? Math.floor(result) : Math.ceil(result);		
		
		
		x = xBeg, y = yBeg + r;
		var minusPos = x - (maxBit+2) * r;
		this.rightAlign(minuend, x, y, r);
		
		decimalString = minuendDecimalPart.toFixed(precision);
		decimalPointPos = decimalString.indexOf('.');
		if (decimalPointPos != -1) {
			decimalString = decimalString.substr(decimalPointPos+1, precision);
			minuendDecimalPart = parseInt(decimalString);
			plot.fillText('.', x, y+0.4*r, r);
			this.leftAlign(minuendDecimalPart, x + r, y , r);
		}
		
		y += 1.5 * r;
		this.rightAlign(subtrahend, x, y, r);
		
		decimalString = subtrahendDecimalPart.toFixed(precision);
		decimalPointPos = decimalString.indexOf('.');
		if (decimalPointPos != -1) {
			decimalString = decimalString.substr(decimalPointPos+1, precision);
			subtrahendDecimalPart = parseInt(decimalString);
			plot.fillText('.', x, y+0.4*r, r);
			this.leftAlign(subtrahendDecimalPart, x + r, y , r);
		}
			
		plot.setFont('normal normal normal '+r.toFixed(0)+'px'+ ' arial')
			.fillText('-', minusPos, y+0.4*r, r);
		
		y += r;
		plot.beginPath()
			.moveTo(minusPos - r, y)
			.lineTo(x + (precision+ 2) *r, y)
			.closePath()
			.stroke();
			
		y += r;
		this.rightAlign(result, x, y, r);
		
		if (result < 0) {
			plot.fillText('-', minusPos, y+0.2*r, r);
		}
		
		decimalString = resultDecimalPart.toFixed(precision);
		decimalPointPos = decimalString.indexOf('.');
		if (decimalPointPos != -1) {
			decimalString = decimalString.substr(decimalPointPos+1, precision);
			resultDecimalPart = parseInt(decimalString);
			plot.fillText('.', x, y+0.4*r, r);
			this.leftAlign(resultDecimalPart, x + r, y , r);
		}
			
			
		plot.restore();
	}</span>

<span style="font-size:18px;">function myDraw() {  
    var config = new PlotConfiguration();  
    config.init();  
    config.setPreference(); 
	//config.setSector(1,1,1,1);
 
    //config.axis2D(0, 0, 180);  	
	
	
	var vertExp = new VerticalExpression();
	
	var x = 300, y = 20, r = 20;
	
	
	vertExp.floatAdd(1.23, 20.54, 2, x, y , r);
	
	y += 200;
	vertExp.floatSub(1.23, 20.54, 2, x, y , r);

	
}</span>

本节到此结束，欲知后事如何，请看下回分解。