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对数的首数、尾数对初中学生来说是两个重要而又难理解的概念,课本中先通过由特殊到一般规律得出结论:“所有正数的对数都可以写成一个整数加上一个正的纯小数(或者零)的形式。整数部分叫做这个对数的首数;正的纯小数(或者零)部分叫做这个对数的尾数。”建议在教学时对上述结论进行一般化的验证,学生是可以接受的。即对任给正数N,令N=a×10~n(1≤a<10,n为整数)。两边取以10为底的对数得 1gN=1g(a×10~n)=n+lga ∵1≤a<10。∴lgl≤lga<1g10即0≤lga<1因此lga是正的纯小数(或者零)。于是1gN是
The first number and the mantissa of the logarithm are two important and incomprehensible concepts for junior high school students. In the textbook, we first draw the conclusion from the special to the general rule: “The logarithm of all positive numbers can be written as an integer plus A positive fractional (or zero) form. The integer part is called the first number of the logarithm; the positive fractional (or zero) part is called the mantissa of the logarithm." It is recommended that the above conclusion be generalized in teaching. Verify that students are acceptable. That is, for any given positive number N, let N=a×10~n (1≤a<10, n is an integer). Take the base 10 logarithm of both sides 1gN=1g(a×10~n)=n+lga ∵1≤a<10. ∴lgl≤lga<1g10, ie, 0≤lga<1, so lga is a positive pure decimal (or zero). So 1gN is