Advantages of the Place Value System 1

The Decimal Place Value System has now been accepted all over the world. One of the reasons the way it simplifies many operations related to numbers. Let us see some of these in detail.

Simple algorithms for 4 operations

Thinking about a number in terms of groups of ten and powers of ten, makes the Place Value System an algebraic way of representing numbers.

34567 = 3x4 + 4x3 + 5x2 + 6x1 + 7x0 where x = 10.

This algebraic structure makes algorithms for arithmetic operations easy for a common people to master. Addition or subtraction of any number can be broken down into adding and subtracting of the numerals in the different (place) places. This is the main reason for it to be adopted by all modern civilizations.

The invention and adoption of this system may also indicate an inclination for the human brain to understand algebraic structures.

Documentation of Computations

Another advantage was that all computations can be documented step by step.

In his book Liber Abaci, Leonardo of Pisa, drawing on examples from business and everyday life, showcased how these tools could be used to perform standard arithmetic calculations and solve business problems such as the splitting of profits.

Merchants & accountants readily adapted this method since this helped them to auditing & checking past transactions. Hence it spread very rapidly.

Mechanization of Computation

The Place Value System also allows "mechanisation" of computational algorithms. In the 1650s, the mathematician Blaise Pascal developed a mechanical calculator for adding & subtracting numbers using gears 10 teeth. Today these skills have become part of the primary school math curriculum.

Today computational algorithms have been coded in software so that even wrist watches and mobile phones can calculate!

Place Value System & Modern Science

Modern science is generally accepted to have started with Kepler's discovery of the elliptical orbits of planets. This discovery was the result of enormous amounts of calculations Kepler did using Tycho Brahe's celestial observations. It is accepted that Kepler was able to perform these calculations because of the algorithms developed from the Place Value System!

Metric System of Measurements

The Decimal System could represent any magnitude from the smallest (atomic distances) to the largest (distances in the Universe).

Hence it was so easy that all units of measurements have been worked out using its framework. Internationally it is called Metric System.

In weight we have Kilogram (1000 g), g etc.

In distance we have Kilometre (1000 m), m, cm, mm etc.

It has been extended to measure fractional magnitudes also.

Modified Metric System in money transactions

The advantages of making money denominations mirroring the metric system was seen immediately.

US was the first country to decimalize currency in 1792 through the Coinage Act of 1792. Many countries followed and today it is almost the international standard.

In money, apart from 100, 10 and 1 rupee notes, we also have other denominations. This is because unlike other measures, money is used for daily transactions and for all kinds of values. Hence having other denominations like 2, 5, 50, 500 etc makes it easier to pay out various amounts.

Continuance of older systems

In many measures like weight, volume and distance a few countries and many humans continue to use other units like feet, pound, gallon etc. This is because the long association of these units have given many a feeling of "comfort" deeply etched in their conscience.

The measurement of time has also resisted introduction of the metric system. France introduced such a system which had to be dropped after a few years since most of its citizens resisted it.

But even in time, time intervals shorter than the second and longer than a year use the metric system.