Solve left|1.2*10^-2-1.146*10^-5right|^2

$${ \left| 1.2 \times { 10 }^{ -2 } -1.146 \times { 10 }^{ -5 } \right| }^{ 2 }$$

Evaluate

$$0.0001437250913316$$

Solution Steps

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\left(|1.2\times \frac{1}{100}-1.146\times 10^{-5}|\right)^{2}$$

Multiply 1.2 and \frac{1}{100} to get \frac{3}{250}.

$$\left(|\frac{3}{250}-1.146\times 10^{-5}|\right)^{2}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\left(|\frac{3}{250}-1.146\times \frac{1}{100000}|\right)^{2}$$

Multiply 1.146 and \frac{1}{100000} to get \frac{573}{50000000}.

$$\left(|\frac{3}{250}-\frac{573}{50000000}|\right)^{2}$$

Subtract \frac{573}{50000000} from \frac{3}{250} to get \frac{599427}{50000000}.

$$\left(|\frac{599427}{50000000}|\right)^{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{599427}{50000000} is \frac{599427}{50000000}.

$$\left(\frac{599427}{50000000}\right)^{2}$$

Calculate \frac{599427}{50000000} to the power of 2 and get \frac{359312728329}{2500000000000000}.

$$\frac{359312728329}{2500000000000000}$$

Factor

$$\frac{3 ^ {6} \cdot 149 ^ {4}}{2 ^ {14} \cdot 5 ^ {16}} = 0.0001437250913316$$