This arrangement is necessary because of the inherent properties of numbers as expressed in figures, under what we call our decimal system, which means simply the practice we have adopted of expressing our numbers in multiples of ten. This arose from the fact that we happen to be born with ten fingers, and our ancestors, like our children, learned to count by means of those very useful “markers.” In the system of counting every place, or column, counting from the right, has a value ten times greater than the one in the place or column nearest on the right. Thus in the number 36,542 the first figure on the right represents “ones,” the next ten times as much or “tens,” the next ten times as much again or “hundreds,” and so on. We really read this number backward when we name it, for in handling it in any way we have to start with the last figure, representing the “ones.” The number really means two ones, four tens, five hundreds, six thousands and three ten thousands. It is built up this way, really by addition: 2 40 500 6000 30000 ------ 36,542 Now, this principle underlies the processes called “carrying” and “borrowing.” You wish to add 26 and 37. Adding the 6 ones to the 7 you get 13 ones, or 3 ones and 1 ten. So you “carry” that 1 ten to the column where it belongs, leaving the 3 ones in =their= proper column. Thus, in your tens column you have 2 tens plus 3 tens plus the 1 ten “carried,” which makes 6 tens; and your result is 63, or 6 tens and 3 ones. Again, you want to subtract 19 from 38. As you cannot take 9 from 8, you “borrow” one of the 3 tens, making your 8 into 18 and subtract 9 from that, leaving 9. By so doing you have left but 2 tens in your tens column, and so there your subtraction is now from 2, leaving 1. Hence your result is 9 ones and 1 ten, or 19. Here is an example in subtraction which was once used, and which is as likely to trip one up as any that could be set. Subtract 199,999 from 320,012. The result is as follows: 320,012 199,999 ------- 120,013 Now, you cannot take 9 from 2, so you “borrow” one from the left and make your two 12. Then 9 from 12 leaves 3. In borrowing from the left you reduce the 1 in the tens column to 0. As you cannot take 9 from 0, you must again borrow from the left. But what are you to borrow from? In the third, or hundreds column there is only a 0. Hence, before you can borrow from this column you must make this 0 a 10 by borrowing from the fourth, or thousands column (counting your columns always from the right). But again here you find only a 0, and so before you can make even this “borrow” you must borrow one from the 2 in the ten thousands column. Now see what happens. With the one which you have finally borrowed you have made the 0 left in the second or tens column into a 10, and you take 9 from 10, which leaves 1.