 The Hindu-Arabic number system has some interesting properties, here's one of them. Multiply 9 times any number, say 983,264. Pick one of the digits in the product. We'll pick the number 7. Now add up the remaining digits. If the answer has more than one digit, add them. Repeat the process until you get down to a single digit. Subtract that digit from 9, and you get the number you picked out of the original product. This will work no matter which digit you choose to remove from the product. It's the base 10 system that makes this work. For example, we can write the number ABCDEF as the sum of its positional digits. With this view, we can see that the numbers 2, 5, and 10 divide evenly into each of the terms, except possibly the last digit, F. This is why, if the last digit is even, the whole number is even. If the last digit is odd, the whole number is odd. If the last digit is divisible by 5, then the whole number is divisible by 5. And if the last digit is 0, the whole number is divisible by 10. Moving on a bit, we can rewrite this number by breaking up the powers of 10, subtracting and adding 1 to each of them. Multiplying each digit through the sum and rearranging, we get this. Every number in the first bracket is divisible by 9. So if the sum of the digits in the second bracket is also divisible by 9, the whole number is divisible by 9. Furthermore, if the sum in the second bracket is not divisible by 9, then the whole number is not divisible by 9. By the way, the same thing is true for 3. So in our missing digit exercise, we multiplied a number by 9, guaranteeing that the sum of the product's digits would add up to 9. Now pulling out any digit will reduce the remaining sum by just that amount. So subtracting it from 9 gives you the removed digit. This system is easily extended into the decimal number system by dividing by 10 for each position to the right of the decimal point in much the same way we multiplied by 10 for positions to the left. We write abc.efg as this. For example, 0.75 is 7 over 10 plus 5 over 100, or 3 fourths.