Solve 1/4+3*1/16+8/64+3*1/256+3*frac{1}{1024}

$$\frac { 1 } { 4 } + 3 \times \frac { 1 } { 16 } + \frac { 8 } { 64 } + 3 \times \frac { 1 } { 256 } + 3 \times \frac { 1 } { 1024 }$$

Evaluate

$$\frac{591}{1024}\approx 0.577148438$$

Solution Steps

Multiply 3 and \frac{1}{16} to get \frac{3}{16}.

$$\frac{1}{4}+\frac{3}{16}+\frac{8}{64}+3\times \frac{1}{256}+3\times \frac{1}{1024}$$

Least common multiple of 4 and 16 is 16. Convert \frac{1}{4} and \frac{3}{16} to fractions with denominator 16.

$$\frac{4}{16}+\frac{3}{16}+\frac{8}{64}+3\times \frac{1}{256}+3\times \frac{1}{1024}$$

Since \frac{4}{16} and \frac{3}{16} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{16}+\frac{8}{64}+3\times \frac{1}{256}+3\times \frac{1}{1024}$$

Add 4 and 3 to get 7.

$$\frac{7}{16}+\frac{8}{64}+3\times \frac{1}{256}+3\times \frac{1}{1024}$$

Reduce the fraction \frac{8}{64} to lowest terms by extracting and canceling out 8.

$$\frac{7}{16}+\frac{1}{8}+3\times \frac{1}{256}+3\times \frac{1}{1024}$$

Least common multiple of 16 and 8 is 16. Convert \frac{7}{16} and \frac{1}{8} to fractions with denominator 16.

$$\frac{7}{16}+\frac{2}{16}+3\times \frac{1}{256}+3\times \frac{1}{1024}$$

Since \frac{7}{16} and \frac{2}{16} have the same denominator, add them by adding their numerators.

$$\frac{7+2}{16}+3\times \frac{1}{256}+3\times \frac{1}{1024}$$

Add 7 and 2 to get 9.

$$\frac{9}{16}+3\times \frac{1}{256}+3\times \frac{1}{1024}$$

Multiply 3 and \frac{1}{256} to get \frac{3}{256}.

$$\frac{9}{16}+\frac{3}{256}+3\times \frac{1}{1024}$$

Least common multiple of 16 and 256 is 256. Convert \frac{9}{16} and \frac{3}{256} to fractions with denominator 256.

$$\frac{144}{256}+\frac{3}{256}+3\times \frac{1}{1024}$$

Since \frac{144}{256} and \frac{3}{256} have the same denominator, add them by adding their numerators.

$$\frac{144+3}{256}+3\times \frac{1}{1024}$$

Add 144 and 3 to get 147.

$$\frac{147}{256}+3\times \frac{1}{1024}$$

Multiply 3 and \frac{1}{1024} to get \frac{3}{1024}.

$$\frac{147}{256}+\frac{3}{1024}$$

Least common multiple of 256 and 1024 is 1024. Convert \frac{147}{256} and \frac{3}{1024} to fractions with denominator 1024.

$$\frac{588}{1024}+\frac{3}{1024}$$

Since \frac{588}{1024} and \frac{3}{1024} have the same denominator, add them by adding their numerators.

$$\frac{588+3}{1024}$$

Add 588 and 3 to get 591.

$$\frac{591}{1024}$$

Factor

$$\frac{3 \cdot 197}{2 ^ {10}} = 0.5771484375$$