Solve 4/5+4/25+4/125+4/625+frac{9}{3125}

$$\frac{ 4 }{ 5 } + \frac{ 4 }{ 25 } + \frac{ 4 }{ 125 } + \frac{ 4 }{ 625 } + \frac{ 9 }{ 3125 }$$

Evaluate

$$\frac{3129}{3125}=1.00128$$

Solution Steps

Least common multiple of 5 and 25 is 25. Convert \frac{4}{5} and \frac{4}{25} to fractions with denominator 25.

$$\frac{20}{25}+\frac{4}{25}+\frac{4}{125}+\frac{4}{625}+\frac{9}{3125}$$

Since \frac{20}{25} and \frac{4}{25} have the same denominator, add them by adding their numerators.

$$\frac{20+4}{25}+\frac{4}{125}+\frac{4}{625}+\frac{9}{3125}$$

Add 20 and 4 to get 24.

$$\frac{24}{25}+\frac{4}{125}+\frac{4}{625}+\frac{9}{3125}$$

Least common multiple of 25 and 125 is 125. Convert \frac{24}{25} and \frac{4}{125} to fractions with denominator 125.

$$\frac{120}{125}+\frac{4}{125}+\frac{4}{625}+\frac{9}{3125}$$

Since \frac{120}{125} and \frac{4}{125} have the same denominator, add them by adding their numerators.

$$\frac{120+4}{125}+\frac{4}{625}+\frac{9}{3125}$$

Add 120 and 4 to get 124.

$$\frac{124}{125}+\frac{4}{625}+\frac{9}{3125}$$

Least common multiple of 125 and 625 is 625. Convert \frac{124}{125} and \frac{4}{625} to fractions with denominator 625.

$$\frac{620}{625}+\frac{4}{625}+\frac{9}{3125}$$

Since \frac{620}{625} and \frac{4}{625} have the same denominator, add them by adding their numerators.

$$\frac{620+4}{625}+\frac{9}{3125}$$

Add 620 and 4 to get 624.

$$\frac{624}{625}+\frac{9}{3125}$$

Least common multiple of 625 and 3125 is 3125. Convert \frac{624}{625} and \frac{9}{3125} to fractions with denominator 3125.

$$\frac{3120}{3125}+\frac{9}{3125}$$

Since \frac{3120}{3125} and \frac{9}{3125} have the same denominator, add them by adding their numerators.

$$\frac{3120+9}{3125}$$

Add 3120 and 9 to get 3129.

$$\frac{3129}{3125}$$

Factor

$$\frac{3 \cdot 7 \cdot 149}{5 ^ {5}} = 1\frac{4}{3125} = 1.00128$$