Solve 11800*(1+10^2/1)^-1+13*10*(1+10^3)^-2

$$11800 \times ( 1 + 10 ^ { 2 } / 1 ) ^ { - 1 } + 13 \times 10 \times ( 1 + 10 ^ { 3 } ) ^ { - 2 }$$

Evaluate

$$\frac{909509610}{7784777}\approx 116.831812909$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$11800\left(1+\frac{100}{1}\right)^{-1}+13\times 10\left(1+10^{3}\right)^{-2}$$

Anything divided by one gives itself.

$$11800\left(1+100\right)^{-1}+13\times 10\left(1+10^{3}\right)^{-2}$$

Add 1 and 100 to get 101.

$$11800\times 101^{-1}+13\times 10\left(1+10^{3}\right)^{-2}$$

Calculate 101 to the power of -1 and get \frac{1}{101}.

$$11800\times \frac{1}{101}+13\times 10\left(1+10^{3}\right)^{-2}$$

Multiply 11800 and \frac{1}{101} to get \frac{11800}{101}.

$$\frac{11800}{101}+13\times 10\left(1+10^{3}\right)^{-2}$$

Multiply 13 and 10 to get 130.

$$\frac{11800}{101}+130\left(1+10^{3}\right)^{-2}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{11800}{101}+130\left(1+1000\right)^{-2}$$

Add 1 and 1000 to get 1001.

$$\frac{11800}{101}+130\times 1001^{-2}$$

Calculate 1001 to the power of -2 and get \frac{1}{1002001}.

$$\frac{11800}{101}+130\times \frac{1}{1002001}$$

Multiply 130 and \frac{1}{1002001} to get \frac{10}{77077}.

$$\frac{11800}{101}+\frac{10}{77077}$$

Add \frac{11800}{101} and \frac{10}{77077} to get \frac{909509610}{7784777}.

$$\frac{909509610}{7784777}$$

Factor

$$\frac{2 \cdot 3 \cdot 5 \cdot 563 \cdot 53849}{7 ^ {2} \cdot 11 ^ {2} \cdot 13 \cdot 101} = 116\frac{6475478}{7784777} = 116.83181290870631$$