Solve left|263*10^-2-1.146*10^-5right|^2

$${ \left| 263 \times { 10 }^{ -2 } -1.146 \times { 10 }^{ -5 } \right| }^{ 2 }$$

Evaluate

$$6.9168397205313316$$

Solution Steps

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

$$\left(|263\times \frac{1}{100}-1.146\times 10^{-5}|\right)^{2}$$

Multiply 263 and \frac{1}{100} to get \frac{263}{100}.

$$\left(|\frac{263}{100}-1.146\times 10^{-5}|\right)^{2}$$

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

$$\left(|\frac{263}{100}-1.146\times \frac{1}{100000}|\right)^{2}$$

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

$$\left(|\frac{263}{100}-\frac{573}{50000000}|\right)^{2}$$

Subtract \frac{573}{50000000} from \frac{263}{100} to get \frac{131499427}{50000000}.

$$\left(|\frac{131499427}{50000000}|\right)^{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{131499427}{50000000} is \frac{131499427}{50000000}.

$$\left(\frac{131499427}{50000000}\right)^{2}$$

Calculate \frac{131499427}{50000000} to the power of 2 and get \frac{17292099301328329}{2500000000000000}.

$$\frac{17292099301328329}{2500000000000000}$$

Factor

$$\frac{29 ^ {2} \cdot 31 ^ {2} \cdot 146273 ^ {2}}{2 ^ {14} \cdot 5 ^ {16}} = 6\frac{2292099301328328}{2500000000000000} = 6.916839720531331$$