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Tests of Divisibility - Divisibility by 10

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notes

We first look at some multiples of 10. 
10, 20, 30, 40, 50, 60, ... , 
and then at some non-multiples of 10. 
13, 27, 32, 48, 55, 69, 
From these lists we see that if the ones digit of a number is 0, then the number is a multiple of 10; and if the ones digit is not 0, then the number is not a multiple of 10. So, we get a test of divisibility by 10. 
we must not stop with just stating the test; we must also explain why it “works”. That is not hard to do; we only need to remember the rules of place value. Take the number. ... cba; this is a short form for 
... + 100c + 10b + a 
Here a is the one’s digit, b is the ten’s digit, c is the hundred’s digit, and so on. The dots are there to say that there may be more digits to the left of c. 
Since 10, 100, ... are divisible by 10, so are 10b, 100c, ... . And as for the number a is concerned, it must be a divisible by 10 if the given number is divisible by 10. This is possible only when a = 0. 
Hence, a number is divisible by 10 when its one’s digit is 0.

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