INTRODUCTION
CUTTING CORNERS
Whether due to curiosity or sheer laziness , man has always been expeimenting
, searching for and stumbling up on ways of making work easier for himseif . That anony mous
caveman who chipped the corners off a flat rock and invented the wheel
started this tradition .
Most of man’ s efforts in the past were directed
at con- serving or increasing his muscle power’ but as time went on some
were aimed at saving weat and teat on another vital organ; his brain. It
followed naturally that his attention turned to reducing such laborious tasks as calculating.
WHAT SHORT CUTS ARE
Short cuts in mathematics are
ingenious little tricks in calculating that can save enormous amounts of time
and labour _ not to mention paper – in solving otherwise complicated problems.
There are no magical powers connected with these tricks: each is based on sound
mathematical principals growing out of the very properties of numbers
themselves .The results they produce are absoulutly accurate and inflallible
when applied correctly .Short-cut methods are by no means of recent origin:they
were known even to the ancient Greeks. The supply of Short-cuts is unlimitted.
Many are known ,and many are yet to be discovered. The all shortcuts included
in this page have been selected because they are easy to learn,simple to use
and can be applied to the widest range of calculating problems.
PUTTING NUMBERS IN THEIR PLACE
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 are called digits. Integers are numbers consisting of one or more digits. For example, 72,958 is an integer consisting of five digits, 7,2, 9, 5, and 8. In practice, the word number is applied to many different combinations of digits ranging from whole numbers, to fractions, mixed numbers, and decimals. The word integer, however, applies only to whole numbers.
Each digit in a number has a name based on its position in the number. The number system we are accustomed to dealing with is based on the number 10. Each number position in this system is named for a power of 10. The position immediately to the left of the decimal point of a number is called the units position. In the number 1.4 the digit 1 is in the units position and is called the units digit. In fact, any digit that occupies that position is called the units digit. The next position to the left of the units position is called the tens position, and any digit occupying that space is called the tens digit. In the number 51.4 the 5 is the tens digit. Continuing to the left, in order, are the hundreds, thousands, ten-thousands, hundred-thousands, millions positions, and so on.
The positions of the digits to the right of the decimal point also have names similar to those to the left. The position immediately to the right of the decimal point is called the tenths position. Notice that the name is tenths and not tens. In fact, all positions to the right of the decimal point end in ths. The next position to the right of the tenths position is the hundredths position, then the thousandths position, and, in order, the ten-thousandths, the hundred-thousandths, the millionths.
Why pencil painting on this website?
In order to study and learn lightning mathematics, the mind must be stable in one place without wandering.
The mind should be free from the temptation of dripping no matter how much distraction comes.
Only by learning meditation or painting or both can the messages on this website be imprinted on the mind.
Long live! Grow !!
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