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The decimal system was found to be very easy & convenient for calculations & conversions. Hence it has been adopted by almost all countries as the standard system for referring to any measurement. It is now called the “International System of Units” or SI. In common parlance it is also referred to as “metric system”.
The only 3 countries which have not adopted SI are USA, Myanmar & Liberia.
There are separate “names” for each power of 10, as shown below.
Scientific Measurements
For scientific measurements which can vary from the smallest to the highest, like in Data & Frequency, this nomenclature is fully used. In fact, more “names” have been invented to refer to quantities which do not fall in this range. Mega, Giga & Nano are examples.
Daily Life Measurements
But for most measurements used frequently in daily, only some of the names are commonly used.
Money – Rupee & Paise. Technically a Paise is a Centi Rupee.
Length/Distance – Meter, Centimeter & Kilometer
Volume – Liter, Millilitre
Weight – Kilogram & Gram. Mega gram (1000 kgs) is called Tonne
Temperature – Degree Centigrade
Area - The basic unit “Are” which is equal to 100 square meters, is very rarely used. A hundred “are”s is called Hectare
Data – for convenience of computer storage, a Kilo, when it refers to data, is actually 1024.
Interpreting 5.738 meters
Imagine we want to measure the length of a corridor in the school in meters and fractions of a meter.
Assume we have a Meter Ruler, a ruler which is 1/10 of a meter which we can call Decimeter, a ruler which is 1/100 of a meter which we can call Centimeter and a ruler which is 1/1000 of a meter which we call Millimeter.
To measure the distance, we first mark off with Meter Ruler until we arrive at a distance which is less than a meter from the end. Assume that there were 5 meters.
Then we use a decimeter to mark off the balance distance until we arrive at a distance which is less than a decimeter. Assume there were 7 Decimeters.
Assume that we find there are 3 centimeters, and the final bit is equal to 8 Millimeters.
Then we can write the distance in meters as 5.738.
Decimal Fractions and Measurement Accuracy
Mathematically 4.2 = 4.20 = 4.200.
But from the perspective of measurements 4.2 is different from 4.20 and different from 4.200.
4.2 implies that a certain quantity has been measured with a scale which is divided only in tenths i.e 0.1 i.e the reading falls between 4.1 and 4.3.
4.20 implies that it has been measured with a scale which is divided in hundredths i.e 0.01 and the reading falls between 4.19 and 4.21.
4.200 implies that it has been measured with a scale which is divided in thousandths i.e 0.001 and the reading falls between 4.199 and 4.201.
Obviously 4.200 is a more accurate measure than 4.2 or 4.20. 4.20 is better than 4.2.
Percentage
In commercial transactions, another form of decimal fractions is used by convention. Normal interpretation of decimal fractions assume that the whole is 1. In percentages, the whole is taken to be 100.
0.5 is the same as 50 out of 100. It is written as 50%, where % is pronounced as “percent”. Cent stands for century, which is another name for 100. 50% indicates 50 per 100.
We will see more about percentages when we study application of math in commercial transactions.
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