Work With Numbers, Not Digits

This rule, agreed on by almost every teacher of short-cut mathematics, is to work from left to right - not right to left.

This is just opposite to what is taught in school. We are taught to add, subtract, and multiply from right to left. It is easier to teach to children and easier to learn from the "imitation" standpoint of learning by rote, but it is directly contrary to the way we read and think about numbers.

There are at least three important advantages to working from left to right.

First, it is the way we look at everything else on a page. We read from left to right.

Second, it is the way we look at a number right up to the moment we begin doing something to it. For instance, look at the number 164,928. You read it one-hundred sixty-four thousand, nine-hundred and twenty-eight. But when you begin to add or subtract or multiply it, you are taught to tackle it as 8, 2, 9, 4, 6, 1.

It isn't the same number at all. At the very outset we are taught to combine this number with another in a totally foreign, unrecognizable form.

There is still a third reason why it is faster and better to work from left to right. You develop your most important numbers first and work toward the "details."

Suppose you are a salesman who has just sold a $423 order for which you will get a 6% commission. If you work from left to right you know by the time you get just one digit that your commission will be twenty-something dollars. You know when you have finished two digits that your commission is $25 and change.

But if you work in the schoolroom, right-to-left way, the first two digits you develop tell you only the change. You know only that you will get something dollars and 38 cents. Not until you finish working out the whole commission do you know that your commission will be $25.38.

This is true of every number and every application, whether or not a decimal point happens to break it into dollars and cents. The first digit in a number is ten times as important as the second, a hundred times as important as the third, and so on down the line.

Working from left to right reveals to you, step by step, the most important numbers first. For this reason alone, the new methods for doing this are one of the most valuable quick estimating tools you can have.

The fact that each digit in a number decreases in importance by a factor of ten as it moves one place to the right is the reason why many companies today report their operations and financial position in "round" numbers: rounding off the pennies or, in very large companies, tens, hundreds, and even thousands of dollars. It is the number to the left that is most important.

Even the U. S. government now permits each of us to figure our income tax in round numbers, to the nearest dollar for each deduction and part of the calculation. If your income-tax report is at all complicated and you do it yourself and have not tried rounding it off, you will be astonished next time you do it. It saves close to half the time of doing the report.

The point to be made here is simply this: work at it. It is, as you learn to use it, as black-and-white a difference as thinking of the number 462 or approaching it as 2, 6, 4.