### Playing with Numbers

In this session, I will discuss more about numbers. Starting with numbers in general form: To understand this, let’s take a number: 52. If I break it down, what’s the meaning of breaking down? I can write 52 as “Fifty” plus “Two”. This is a two digit number. 2 is at the unit’s place, and 5 is at 10’s place, I’m sure all of you know this. So I can write the same 52 as “Five” into “Ten”, because “Five” is at 10’s place, plus “Two” into “One”, because “Two” is at 1’s place. So you can represent 52 as 5 into 10 plus 2 into 1.

Let’s take one more example, let’s take 37. So how do I write in this format? 37 can be written as, since 3 is at 10’s place, or the place value is 10, we will write 3 into 10 plus 7 into 1. So 37 is 3 into 10 plus 7 into 1. Why 7 into 1? Because 7 is at 1’s place. All of you know writing numbers in this way. Now, instead of numbers, if I want to generalize and take any two digit number, I’ll, instead of using any two digits, I’ll use any two digits, what’s the meaning of “any two digits”. It’s “a b”. So if I take two digit number “a b”, I can write this as, a is at 10’s place, and b is at 1’s place. I can write this as 10a plus 1b. Instead of “a b”, let’s say if it is b a, then it will become 10 into b plus 1 into a. This is how we represent any two digit number. Right? By using variables, right? Meaning of “any” is nothing but, In Math, we can use variables. So, this “a” is a single digit, “b” is also a single digit when I represent “a b” as any two digit number, “a” and “b” can represent digits from 0 to 9. Now, let’s take a 3 digit number, let’s take 356. How do I write 356? I can break it down as “Three Hundred” plus “Fifty” plus “Six”. Now “3” is at 100’s place, so I can write “100 into 3” plus, “5” is at 10’s place, that’s “10 into 5” plus, “6” is at 1’s place, that’s “1 into 6”. In a similar fashion, we can write 427 as “100 into 4”, “2 into 10” or “10 into 2” to follow the order “100 into 10” plus “10 into 2” plus “1 into 7”. That’s how we can break down 427.

In general, a three digit number “ABC” can be, “ABC” which is made up of digits “A”, “B” and “C” can be written as “ABC” equal to “100 A” plus “10 B” plus “1 C”. Because “A” is at 100’s place, “B” is at 10’s place, and “C” is at 1’s place. Same way, suppose it is “CAB” how will I write? “100 C” plus “10 A” plus “1 B”. Or “CBA” can be written as “100 C” plus “10 B” plus “1 A”.