Solve 100*1-{left(frac{1/2right)}^10}{1-1/2}*2-100

$$100 \times \frac{ 1- { \left( \frac{ 1 }{ 2 } \right) }^{ 10 } }{ 1- \frac{ 1 }{ 2 } } \times 2-100$$

Evaluate

$$\frac{19175}{64}=299.609375$$

Solution Steps

Calculate \frac{1}{2} to the power of 10 and get \frac{1}{1024}.

$$100\times \frac{1-\frac{1}{1024}}{1-\frac{1}{2}}\times 2-100$$

Convert 1 to fraction \frac{1024}{1024}.

$$100\times \frac{\frac{1024}{1024}-\frac{1}{1024}}{1-\frac{1}{2}}\times 2-100$$

Since \frac{1024}{1024} and \frac{1}{1024} have the same denominator, subtract them by subtracting their numerators.

$$100\times \frac{\frac{1024-1}{1024}}{1-\frac{1}{2}}\times 2-100$$

Subtract 1 from 1024 to get 1023.

$$100\times \frac{\frac{1023}{1024}}{1-\frac{1}{2}}\times 2-100$$

Convert 1 to fraction \frac{2}{2}.

$$100\times \frac{\frac{1023}{1024}}{\frac{2}{2}-\frac{1}{2}}\times 2-100$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$100\times \frac{\frac{1023}{1024}}{\frac{2-1}{2}}\times 2-100$$

Subtract 1 from 2 to get 1.

$$100\times \frac{\frac{1023}{1024}}{\frac{1}{2}}\times 2-100$$

Divide \frac{1023}{1024} by \frac{1}{2} by multiplying \frac{1023}{1024} by the reciprocal of \frac{1}{2}.

$$100\times \frac{1023}{1024}\times 2\times 2-100$$

Express \frac{1023}{1024}\times 2 as a single fraction.

$$100\times \frac{1023\times 2}{1024}\times 2-100$$

Multiply 1023 and 2 to get 2046.

$$100\times \frac{2046}{1024}\times 2-100$$

Reduce the fraction \frac{2046}{1024} to lowest terms by extracting and canceling out 2.

$$100\times \frac{1023}{512}\times 2-100$$

Express 100\times \frac{1023}{512} as a single fraction.

$$\frac{100\times 1023}{512}\times 2-100$$

Multiply 100 and 1023 to get 102300.

$$\frac{102300}{512}\times 2-100$$

Reduce the fraction \frac{102300}{512} to lowest terms by extracting and canceling out 4.

$$\frac{25575}{128}\times 2-100$$

Express \frac{25575}{128}\times 2 as a single fraction.

$$\frac{25575\times 2}{128}-100$$

Multiply 25575 and 2 to get 51150.

$$\frac{51150}{128}-100$$

Reduce the fraction \frac{51150}{128} to lowest terms by extracting and canceling out 2.

$$\frac{25575}{64}-100$$

Convert 100 to fraction \frac{6400}{64}.

$$\frac{25575}{64}-\frac{6400}{64}$$

Since \frac{25575}{64} and \frac{6400}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25575-6400}{64}$$

Subtract 6400 from 25575 to get 19175.

$$\frac{19175}{64}$$

Factor

$$\frac{5 ^ {2} \cdot 13 \cdot 59}{2 ^ {6}} = 299\frac{39}{64} = 299.609375$$