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For repeating patterns that begin immediately after the decimal point, the result of the conversion is the fraction with the pattern as a numerator, and the same number of nines as a denominator. For example: 0. 5 = 5/9 0. 62 = 62/99 0. 264 = 264/999 0. 6291 = 6291/9999
The final conversion is from binary to decimal fractions. The only difficulty arises with repeating fractions, but otherwise the method is to shift the fraction to an integer, convert it as above, and then divide by the appropriate power of two in the decimal base. For example:
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
Any such decimal fraction, i.e.: d n = 0 for n > N, may be converted to its equivalent infinite decimal expansion by replacing d N by d N − 1 and replacing all subsequent 0s by 9s (see 0.999...). In summary, every real number that is not a decimal fraction has a unique infinite decimal expansion.
To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is: 50 / 100 × 40 / 100 = 0.50 × 0.40 = 0.20 = 20 / 100 = 20%. It is not correct to divide by 100 and use the percent sign at the same time; it would literally imply ...
That is, the value of an octal "10" is the same as a decimal "8", an octal "20" is a decimal "16", and so on. In a hexadecimal system, there are 16 digits, 0 through 9 followed, by convention, with A through F. That is, a hexadecimal "10" is the same as a decimal "16" and a hexadecimal "20" is the same as a decimal "32".
In the case of the mechanical calculators, the exponent is often treated as side information that is accounted for separately. The IBM 650 computer supported an 8-digit decimal floating-point format in 1953. [1] The otherwise binary Wang VS machine supported a 64-bit decimal floating-point format in 1977. [2]
In 1985, CI launched a calculator for the construction industry called the Construction Master [49] which came preprogrammed with common construction calculations (such as angles, stairs, roofing math, pitch, rise, run, and feet-inch fraction conversions). This would be the first in a line of construction related calculators.
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