Solve left|0510^-9/0301210^-5right|*100^2

$$\left| \frac{ 05 { 10 }^{ -9 } }{ 03012 { 10 }^{ -5 } } \right| \times { 100 }^{ 2 }$$

Evaluate

$$\frac{5}{3012}\approx 0.001660027$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$|\frac{5}{3012\times 10^{4}}|\times 100^{2}$$

Calculate 10 to the power of 4 and get 10000.

$$|\frac{5}{3012\times 10000}|\times 100^{2}$$

Multiply 3012 and 10000 to get 30120000.

$$|\frac{5}{30120000}|\times 100^{2}$$

Reduce the fraction \frac{5}{30120000} to lowest terms by extracting and canceling out 5.

$$|\frac{1}{6024000}|\times 100^{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{1}{6024000} is \frac{1}{6024000}.

$$\frac{1}{6024000}\times 100^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$\frac{1}{6024000}\times 10000$$

Multiply \frac{1}{6024000} and 10000 to get \frac{5}{3012}.

$$\frac{5}{3012}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3 \cdot 251} = 0.0016600265604249668$$