Solve 1000*10*10^-4*1.5/1-1000*1.5*10^-4=

$$\frac { 1000 \cdot 10 \cdot 10 ^ { - 4 } \cdot 1.5 } { 1 - 1000 \cdot 1.5 \cdot 10 ^ { - 4 } } =$$

Evaluate

$$\frac{30}{17}\approx 1.764705882$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$\frac{1000\times 10^{-3}\times 1.5}{1-1000\times 1.5\times 10^{-4}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{1000\times \frac{1}{1000}\times 1.5}{1-1000\times 1.5\times 10^{-4}}$$

Multiply 1000 and \frac{1}{1000} to get 1.

$$\frac{1.5}{1-1000\times 1.5\times 10^{-4}}$$

Multiply 1000 and 1.5 to get 1500.

$$\frac{1.5}{1-1500\times 10^{-4}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{1.5}{1-1500\times \frac{1}{10000}}$$

Multiply 1500 and \frac{1}{10000} to get \frac{3}{20}.

$$\frac{1.5}{1-\frac{3}{20}}$$

Subtract \frac{3}{20} from 1 to get \frac{17}{20}.

$$\frac{1.5}{\frac{17}{20}}$$

Divide 1.5 by \frac{17}{20} by multiplying 1.5 by the reciprocal of \frac{17}{20}.

$$1.5\times \frac{20}{17}$$

Multiply 1.5 and \frac{20}{17} to get \frac{30}{17}.

$$\frac{30}{17}$$

Factor

$$\frac{2 \cdot 3 \cdot 5}{17} = 1\frac{13}{17} = 1.7647058823529411$$