﻿ calculations

## Calculations for item eight of American Scientific page ### Numbers followed by E+… means add noughts to the end until the number of figures after the decimal point is the same as the number after the plus sign, then remove the decimal point. So the greater the number after ‘E’, the larger the amount.

LETTERS

NUMBER OF DIFFERENT COMBINATIONS

### 13 One different combination per second

2.48115E+18 (seconds)

2.48115E+18 / 60 = 4.13525E+16 (minutes)

4.13525E+16 / 60 = 6.89209E+14 (hours)

6.89209E+14 / 24 = 2.8717E+13 (days)

2.8717E+13 / 365.25 = 78,622,990,126 (years)

### The number of possible combinations for the four different letters of DNA (A, C, G, T)

LETTERS

NUMBER OF DIFFERENT COMBINATIONS

LETTERS

NUMBER OF DIFFERENT COMBINATIONS ### 25 4 x 1.1259E+15 =

### 50 5.0706E+30

2.02824E+31

8.11296E+31

3.24519E+32

1.29807E+33

5.1923E+33

2.07692E+34

8.30767E+34

3.32307E+35

1.32923E+36

5.31691E+36

2.12676E+37

8.50706E+37

3.40282E+38

1.36113E+39

5.44452E+39

2.17781E+40

8.71123E+40

3.48449E+41

1.3938E+42

5.57519E+42

2.23007E+43

8.9203E+43

3.56812E+44

1.42725E+45

### 75 5.70899E+45

2.2836E+46

9.13439E+46

3.65375E+47

1.4615E+48

5.84601E+48

2.3384E+49

9.35361E+49

3.74144E+50

1.49658E+51

5.98631E+51

2.39452E+52

9.5781E+52

3.83124E+53

1.5325E+54

6.12998E+54

2.45199E+55

9.80797E+55

3.92319E+56

1.56928E+57

6.2771E+57

2.51084E+58

1.00434E+59

4.01735E+59

1.60694E+60

### 4 x 4.01735E+59 =

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100 ### So 1,000,000,000 in 1.60694E+60 is the same as 1 in 1.60694E+51 With 1.60694E+60 possible combinations, then trying one billion every second takes the following amount of time:

1.60694E+60 / 1,000,000,000 = 1.60694E+51 (seconds)

1.60694E+51 / 60 = 2.67823E+49 (minutes)

2.67823E+49 / 60 = 4.46372E+47 (hours)

4.46372E+47 / 24 = 1.85988E+46 (days)

1.85988E+46 / 365.25 = 5.09208E+43 (years)