6.25 , here 6 is the first digit.
72.5, 7 is the first digit
12.65 1 is the first digit.
We think, all the digits (1 to 9) have equal probabilities to appear as first digit. That is, they has to appear 1 out of 9 times - 11% probability.
But a man, named Benford researched heavily and gave a law. "The 'one' appears as a first digit 30% of the time". The small numbers 1,2,3 appears more as first digit than large numbers like 7,8,9.
Benford law holds good in baseball statistics, area of rivers, population sizes, street address, city populations, super market prices etc.
Let us consider door numbers in a street which has 30 houses.
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19.20,21,22,23,24,25,26,27,28,29,
30.
1 appears 11 times as first digit out of 30. So around 30% times.
Let us say, a price starts at 1 dollar and goes up 10% every time.
1.00.1.10, 1.21,1.33,1.46,1.61,1.77,1.95,2.14,2.36,2.59.....
So naturally 1 appears more times.
SOME PHYSICS CONSTANTS
1. Electronic charge= 1.6021 *10ˆ19 C
2. Magnetic constant= 1.2566...
3. Boltzmann constant =1.3806...
4. Atomic mass constant= 1.6605*10ˆ-27 kg.
5. Atmospheric pressure = 101325 pa
6. Square root of 2 = 1.414
7. Square root of 3 = 1.732
8. Golden ratio =1.618
The human body's vital parameters like, pulse, BP, temperature, oxygen level, waist measurement, sugar level all should be around 100 -one as first digit.
So if you cook up your tax report or balance sheet, a computer software based Benford law will give you away.
According to Benford, the probability of a digit for being a first digit is given below.
1 2 3 4 5 6 7 8 9
30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6%
Small numbers play a major role in our life than large numbers.
We have one sun, one moon and one living planet. Two genders. Three dimensions. Two forms of life- animals and plant. A three letter language called DNA. The most abundant element in the universe is Hydrogen-a one proton -one electron atom. The list goes on.
'One' and 'small numbers' dominate this universe.
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