数学基础计算背诵(小数、分数、平方数、立方数、π).doc

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1、常见分数、小数互化表C列分数化小数的记法：分子乘5，小数点向左移动两位。D、E两列分数化小数的记法：分子乘4，小数点向左移动两位。常用平方数112=121122=144132=169142=196152=225162=256172=289182=324192=361202=400212=441222=484232=529242=576252=625262=676272=729282=784292=841302=900312=961322=1024332=1089342=1156352=1225362=1296372=1369382=1444392=1521402=1600412=168142

2、2=1764432=1849442=1936452=2025462=2116472=2209482=2304492=2401502=2500完全平方数的记忆技巧：(a+b)2=a2+b2+2ab(a－b)2=a2+b2－2ab5五组常见的勾股数：32+42=52；52+122=132；72+242=252；82+152=172；202+212=2925常用立方数53=12563=21673=34383=51293=72911³=133112³=172813³=219714³=274415³=337516³=409617³=491318³=583219³=685921³=9261常用特殊数的乘

3、积25×3＝7525×4＝10025×8＝200125×3＝375125×4＝500125×8＝1000625×16＝1000037×3=111常用的π倍1π3.1411π34.5421π65.942π6.2812π37.6822π69.083π9.4213π40.8223π72.224π12.5614π43.9624π75.365π15.715π47.125π78.56π18.8416π50.2426π81.647π21.9817π53.3827π84.788π25.1218π56.5228π87.929π28.2619π59.6629π91.0610π31.420π62.830π94.2

4、62π113.04112π379.94162π803.8472π153.86122π452.16172π907.4682π200.96132π530.66182π1017.3692π254.34142π615.44192π1133.54102π314152π706.5202π12565速算技巧A×9型A×9=A×10−A743×9=7430−743=6687A×9.9型A×9.9=A×10+A÷10743×9.9=7430−74.3=7355.7A×11型A×11=A×10+A743×11=7430+743=8173A×101型A×101=A×100+A743×101=74300+743=7

5、5043A×5型A×5=10A÷28739.45×5=87394.5÷2=43697.25A÷5型A÷5=0.1A×236.843÷5=3.6843×2=7.3686A×25型A×25=100A÷47234×25=723400÷4=180850A÷25型A÷25=0.01A×43714÷25=37.14×4=148.56A×125型A×125=1000A÷88736×125=8736000÷8=1092000A÷125型A÷125=0.001A×84115÷125=4.115×8=32.92A×1.5型A×1.5=A+A÷23406×1.5=3406＋3406÷2=3406＋1703＝510

6、9“首数相同尾数互补”型乘积积的头＝头×(头+1)积的尾=尾×尾23×27：首数均为2，尾数3＋7=10互补；积的头为2×(2＋1)=6，尾为3×7=21，即621常用的分数、小数及百分数的互化除法除不尽(按四舍五入计算)除法比分数小数百分除法比分数小数百分1÷21:21/20.550%1÷31:31/30.3333%1÷41:41/40.2525%2÷32:32/30.6767%1÷51:51/50.220%1÷61:61/60.1717%2÷52:52/50.440%5÷65:65/60.8383%3÷53:53/50.660%1÷71:71/70.1414%4÷54:54/50.880

7、%2÷72:72/70.2929%1÷81:81/80.12512.5%3÷73:73/70.4343%3÷83:83/80.37537.5%4÷74:74/70.5757%5÷85:85/80.62562.5%5÷75:75/70.7171%7÷87:87/80.87587.5%6÷76:76/70.8686%51÷101:101/100.110%1÷91:91/90.1111%3÷103:103/100.