Solve 2/1.01+102/1.02^2=

$$\frac { 2 } { 1.01 } + \frac { 102 } { 1.02 ^ { 2 } } =$$

Evaluate

$$\frac{515200}{5151}\approx 100.019413706$$

Solution Steps

Expand \frac{2}{1.01} by multiplying both numerator and the denominator by 100.

$$\frac{200}{101}+\frac{102}{1.02^{2}}$$

Calculate 1.02 to the power of 2 and get 1.0404.

$$\frac{200}{101}+\frac{102}{1.0404}$$

Expand \frac{102}{1.0404} by multiplying both numerator and the denominator by 10000.

$$\frac{200}{101}+\frac{1020000}{10404}$$

Reduce the fraction \frac{1020000}{10404} to lowest terms by extracting and canceling out 204.

$$\frac{200}{101}+\frac{5000}{51}$$

Least common multiple of 101 and 51 is 5151. Convert \frac{200}{101} and \frac{5000}{51} to fractions with denominator 5151.

$$\frac{10200}{5151}+\frac{505000}{5151}$$

Since \frac{10200}{5151} and \frac{505000}{5151} have the same denominator, add them by adding their numerators.

$$\frac{10200+505000}{5151}$$

Add 10200 and 505000 to get 515200.

$$\frac{515200}{5151}$$

Factor

$$\frac{7 \cdot 23 \cdot 2 ^ {7} \cdot 5 ^ {2}}{3 \cdot 17 \cdot 101} = 100\frac{100}{5151} = 100.01941370607649$$