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The fourth quotient being 1, we say 333 times 1 is 333, and this plus 22, the numerator of the fraction preceding, is 355; similarly, 106 times 1 is 106, and this plus 7 is 113. In this manner, by employing the four quotients [3;7,15,1], we obtain the four fractions: 3 / 1 , 22 / 7 , 333 / 106 , 355 / 113 , ....
Expanding this form to the six-digit form is as simple as repeating each digit: ... Decimal Fraction 0 00 0 0 3 33 51 0.2 6 66 102 0.4 9 99 153 0.6 C (12) CC 204
The convergents p / q formed by truncating this representation form a sequence of fractions that approximate the square root of two to increasing accuracy, and that are described by the Pell numbers (i.e., p 2 − 2q 2 = ±1).
The first 3 powers of 2 with all but last digit odd is 2 4 = 16, 2 5 = 32 and 2 9 = 512. The next such power of 2 of form 2 n should have n of at least 6 digits. The only powers of 2 with all digits distinct are 2 0 = 1 to 2 15 = 32 768 , 2 20 = 1 048 576 and 2 29 = 536 870 912 .
For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 10 3 = 10 × 10 × 10. More generally, if x = b y, then y is the logarithm of x to base b, written log b x, so log 10 1000 = 3. As a single-variable function, the logarithm to base b is the inverse of exponentiation with base b.
The figure shows that 8 can be decomposed into 5 (the number of ways to climb 4 steps, followed by a single-step) plus 3 (the number of ways to climb 3 steps, followed by a double-step). The same reasoning is applied recursively until a single step, of which there is only one way to climb.
[3] UNU-WIDER data is more complex, total taxes consists of taxes, social contributions, grants receivable, and other revenue. Sources are IMF Country Reports [ 4 ] and OECD Revenue Statistics. [ 5 ]
Inner view of a 1998 Seagate HDD that used the Parallel ATA interface 2.5-inch SATA drive on top of 3.5-inch SATA drive, showing close-up of (7-pin) data and (15-pin) power connectors. Current hard drives connect to a computer over one of several bus types, including parallel ATA, Serial ATA, SCSI, Serial Attached SCSI (SAS), and Fibre Channel.