# Mathedu

Learn math by practice

# Re-engineering Math

## Decimal Metric Systems… and Time Measurement as an Exception

Because we have 10 fingers, the numeration we use is with 10 basis: units, tenth, hundreds, thousands and so on.

And because we count in 10 basis, the International standards for measurement of distance, weight and so on are decimal metric systems.

This means that the different units of distance, for instance, are deduced from one another by a multiplication or division of a power of 10: 10 multiplied by itself a given number of times.

For instance, 1 kilometer is 1,000 meters and 1,000,000 micro-meters, 1 kilo(gram) is 1,000 grams and 1,000,000 milligrams. On the other hand, 1 gram is 1/1,000=0.001 kilo.

The conversions in a decimal metric system does not require complex calculations or a calculator.

This is because the multiplication by a power of ten is either add 0's to the right of an integer, or shift the decimal point to the right (possibly completing with 0's): 1.25 kg=1,250 g.

And the division by a power of 10 is shifting the decimal point to the left after, for an integer, creating a decimal ploint to the right (possibly completing with 0's to the left): 25 g = 0.025 kg.

However, as 10 is only a multiple of 2 and 5, a 1/3 of a kilo is not an exact number of grams, nor even of milligrams. This is because the decimal notation of 1/3 has no end, it is 0.333,333,… For the comparison, 1/2 of a kilo is 500 grams, 1/4 of a kilo is 250 grams.

The exception to the decimal system is time measurement. An hour is divided in 60 minutes and a minute is divided in 60 seconds.

The drawback of that system is that it is rather complicated to convert seconds in minutes and seconds, minutes in hours and seconds, hours in minutes and so on.

The advantage of it is that, as 60 is a multiple of 2, 3, 4, 5 and 6, you may divide a hour by all of these numbers, you get an exact number of minutes: half an hour is 30 minutes, 1/3 of an hour is 20 minutes, 1/4 of an hour is 15 minutes, 1/5 of a hour is 12 minutes and 1/6 of an hour is 10 minutes.

This is a very useful property, isn't it?