(page 1100(2))
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(page 1100(2)) |
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| Another Important Power Series | ||||||||||||||||||||||||||||||||||
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Do you know of another power series that we use? Think about:
The number system we use, called the decimal system, is based on this power series. So what does 1,234 actually mean? 1234 = 1 thousand + 2 hundreds + 3 tens + 4 ones = 1×103 + 2×102 + 3×101 + 4×100We remove the "×10N"s in the above to yield 1234. This is called the positional notation. Most of you probably knew all this, but there's a reason that we are reviewing it, because we're going to look at binary numbers next. But before we leave this page, let us look at the number of moves the monks must make: 18,446,744,073,709,551,615which is more than 1.8 × 1019 or 18 × 1018 or 18 × 109 × 109 or 18 billion billion Once again I need to introduce another notation since mathematicians and other scientists are lazy. Rather than write 1.8 × 1019, we remove the × 10 bit and put the index or exponent after an `E', as in: 1.8 × 1019 = 1.8E19This is referred to as the scientific notation and is often used in calculators. | |||||||||||||||||||||||||||||||||
| hanoi12.qh - 1.5 - 05/10/18 |
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