Thus, the product of 2 x 104 and 3 x 105 equals 6 x 109. If you translate the first two numbers to 20,000 and 300,000, you will see that the product is indeed 6,000,000,000.
2) A number like 2,560,000 can be expressed as 256 x 104, or 25.6 x 105 or 2.56 x 106 or 0.256 x 107. All are the same number, as you can see if you multiply 256 by 10,000: 25.6 by 100,000; 2.56 by 1,000,000; or 0.256 by 10,000,000. Which one of these exponential numbers is it best to use? It is customary to use the one in which the nonexponential portion of the number is between 1 and 10. In the case of 2,560,000, the usual exponential figure is 2.56 x 106. For this reason, in multiplying 2 x 104 by 6 x 105, we present the answer not as 12 x 109, but as 1.2 x 1010. (Where the number 1010 is presented by itself, it is the same as writing 1 x 1010.)
3) The appearance of exponential numbers may be deceiving. 103 is ten times greater than 102. Similarly, 1069 is ten times greater than 1068, despite the fact that intuitively they look about the same. Again, it must be remembered that 1012, for instance, is not twice as great as 106, but a million times as great.
And now we are ready to return to our factorials. If factorial 20 is 2.4 x 1018, you may well hesitate to try to calculate the value of such numbers as factorial 50, factorial 54, factorial 75 and, above all, factorial 539. Fortunately, there exist tables of the lower factorials—say, to factorial 100—and equations whereby the higher factorials can be approximately determined.
Using both tables and equations, the number of combinations possible in hemoglobin can be computed. The answer turns out to be 4 x 10619. If you want to see what that number looks like written out in full, see Figure 9. Let's agree to call 4 x 10619 the "hemoglobin number." Those of you, by the way, who have read Kasner and Newman's "Mathematics and the Imagination" will see that the hemoglobin number is larger than a googol (10100) but smaller than a googolplex (10googol).
| 40, | 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. |
Figure 9. The hemoglobin number.
Of all the hemoglobin number of combinations, only one combination
136
Astounding Science-Fiction
