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100\times \frac{1-\frac{1}{1024}}{1-\frac{1}{2}}-100
Calculate \frac{1}{2} to the power of 10 and get \frac{1}{1024}.
100\times \frac{\frac{1024}{1024}-\frac{1}{1024}}{1-\frac{1}{2}}-100
Convert 1 to fraction \frac{1024}{1024}.
100\times \frac{\frac{1024-1}{1024}}{1-\frac{1}{2}}-100
Since \frac{1024}{1024} and \frac{1}{1024} have the same denominator, subtract them by subtracting their numerators.
100\times \frac{\frac{1023}{1024}}{1-\frac{1}{2}}-100
Subtract 1 from 1024 to get 1023.
100\times \frac{\frac{1023}{1024}}{\frac{2}{2}-\frac{1}{2}}-100
Convert 1 to fraction \frac{2}{2}.
100\times \frac{\frac{1023}{1024}}{\frac{2-1}{2}}-100
Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.
100\times \frac{\frac{1023}{1024}}{\frac{1}{2}}-100
Subtract 1 from 2 to get 1.
100\times \frac{1023}{1024}\times 2-100
Divide \frac{1023}{1024} by \frac{1}{2} by multiplying \frac{1023}{1024} by the reciprocal of \frac{1}{2}.
100\times \frac{1023\times 2}{1024}-100
Express \frac{1023}{1024}\times 2 as a single fraction.
100\times \frac{2046}{1024}-100
Multiply 1023 and 2 to get 2046.
100\times \frac{1023}{512}-100
Reduce the fraction \frac{2046}{1024} to lowest terms by extracting and canceling out 2.
\frac{100\times 1023}{512}-100
Express 100\times \frac{1023}{512} as a single fraction.
\frac{102300}{512}-100
Multiply 100 and 1023 to get 102300.
\frac{25575}{128}-100
Reduce the fraction \frac{102300}{512} to lowest terms by extracting and canceling out 4.
\frac{25575}{128}-\frac{12800}{128}
Convert 100 to fraction \frac{12800}{128}.
\frac{25575-12800}{128}
Since \frac{25575}{128} and \frac{12800}{128} have the same denominator, subtract them by subtracting their numerators.
\frac{12775}{128}
Subtract 12800 from 25575 to get 12775.