Solve 100[1-(1/2)^10]/1-frac{1{2}}

$$\frac { 100 [ 1 - ( \frac { 1 } { 2 } ) ^ { 10 } ] } { 1 - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{25575}{128}=199.8046875$$

Solution Steps

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

$$\frac{100\left(1-\frac{1}{1024}\right)}{1-\frac{1}{2}}$$

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

$$\frac{100\left(\frac{1024}{1024}-\frac{1}{1024}\right)}{1-\frac{1}{2}}$$

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

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

Subtract 1 from 1024 to get 1023.

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

Express 100\times \frac{1023}{1024} as a single fraction.

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

Multiply 100 and 1023 to get 102300.

$$\frac{\frac{102300}{1024}}{1-\frac{1}{2}}$$

Reduce the fraction \frac{102300}{1024} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{25575}{256}}{1-\frac{1}{2}}$$

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

$$\frac{\frac{25575}{256}}{\frac{2}{2}-\frac{1}{2}}$$

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

$$\frac{\frac{25575}{256}}{\frac{2-1}{2}}$$

Subtract 1 from 2 to get 1.

$$\frac{\frac{25575}{256}}{\frac{1}{2}}$$

Divide \frac{25575}{256} by \frac{1}{2} by multiplying \frac{25575}{256} by the reciprocal of \frac{1}{2}.

$$\frac{25575}{256}\times 2$$

Express \frac{25575}{256}\times 2 as a single fraction.

$$\frac{25575\times 2}{256}$$

Multiply 25575 and 2 to get 51150.

$$\frac{51150}{256}$$

Reduce the fraction \frac{51150}{256} to lowest terms by extracting and canceling out 2.

$$\frac{25575}{128}$$

Factor

$$\frac{3 \cdot 5 ^ {2} \cdot 11 \cdot 31}{2 ^ {7}} = 199\frac{103}{128} = 199.8046875$$