What is the power 0 of 10?

Author: idle
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Blog: blog.csdn.net/cg_ I
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Reference books: programmer's mathematics

What is the power 0 of 10?
Reference:In the 10-digit explanation, we have mentioned that "1 is 100 (10 to the power of 0)", that is, 100 = 1.
I still remember what my high school teacher said when he taught us the "exponential law", and also raised the following question: "102 is" Two 10 multiplied ", so 100 is not "0 by 10? In this case, it should not be 1, but 0, right ?"
For me, this is an introverted and real character. Although, the heart is full of questions. I was ashamed to raise a question to the teacher with the aura of authority. I looked at the strong and confident feelings of the students around me, and kept fighting, and even doubted my IQ, with this mentality of "whether it is 1 or 0", I learned a mess in mathematics.
What is the core of this problem? The problem is that "10 N is a multiplication of N 10. When we say "N 10 multiplied", we will naturally make the N phase 1, 2, 3 .... Therefore, when we say "0 by 10", we don't know how to understand it.
So, let's get a definition like "N 10 multiplied. Let's look at how to define 100 in terms of the current knowledge and so on.
As we all know, 103 is 1000,102, 100,101 is 10.
Put these equations together to find their laws.

Every time the number (INDEX) in the top-right corner of 10 is reduced by 1, the number is changed to the original 10 points 1. Therefore, 100 is 1. To sum up, the following rules can be followed when defining a value of 10n (N includes 0:
Each time the index is reduced by 1, the number is changed to 1 in the original 10.
What is 10-1
Do not stop thinking at 100 points. For 10-1 (10 to the power of-1), let us apply this rule (each time the index is reduced by 1, the number is changed to the original 10 points 1 ).

Rule Extension
At first, I set N to 1, 2, 3... 101,102,103... I want to multiply "1x10", "2x10", and "3x10 "......
Then, I threw away the "N 10 multiply" thinking and found an extension rule: For 10 N, Every time n is reduced by 1, it becomes the original 10 points of 1.
When N is 0, it is difficult to apply the rule "10 N is N 10 multiplied. So I turned to "N minus 1, it turns into the original rule of one out of 10" and defined 100 as 1 (because 1 in 10 of 101 is 1 ).
Similarly, the value of 10---3... (that is, when n is-1,-2,-3...) also applies to this extended rule.
In this way, all integers n (...,-3,-2,-, 1, 2, 3,...) can be defined as 10n values. For 10-3, "-3 multiply by 10" thinking and keep watching. However, if an extension rule is applied, even if n is a negative number, it can "define" the n-power value of 10.

Think about N0
It should be emphasized that the value of N0 should not be remembered as a kind of knowledge, but we should also consider how to properly define N0 in order to simplify the rules. This is not a matter of memory, but of imagination. Remember this way of thinking: define values with simplified rules as the goal.