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Later we shall shew you an easier way to convert from octal to decimal fractions. But first we need to explore the octal system itself somewhat more thoroughly. We can use the octal system of writing numbers all by itself, without translating back and forth to the decimal system. We can count and do arithmetic in the octal system, just as we can in the decimal system. It takes a little getting used to, because we are so familiar with decimals, but you will probably be surprised at how rapidly you can learn to use the octal system.
Let’s begin by counting in the octal system. The first eight numbers, including the 0 are the same in octal a in decimal, as shown below:
But when we get to eight, which is the base of the octal system, we meet the first difference. The quantity eight is written as 108 in octal. We can check this and see that it is correct by expanding the octal form:
108 = 1(81) + 0(80) = 1(8) + 0(1) = 8 + 0 = 810.
Thus, we write the quantity as 108 in the octal system. How shall we write the next number, nine, in the octal system?
