Solve left|0.510^-9/0.301210^-5right|*100^2

$$\left| \frac{ 0.5 { 10 }^{ -9 } }{ 0.3012 { 10 }^{ -5 } } \right| \times { 100 }^{ 2 }$$

Evaluate

$$\frac{1250}{753}\approx 1.66002656$$

Solution Steps

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

$$|\frac{0.5}{0.3012\times 10^{4}}|\times 100^{2}$$

Calculate 10 to the power of 4 and get 10000.

$$|\frac{0.5}{0.3012\times 10000}|\times 100^{2}$$

Multiply 0.3012 and 10000 to get 3012.

$$|\frac{0.5}{3012}|\times 100^{2}$$

Expand \frac{0.5}{3012} by multiplying both numerator and the denominator by 10.

$$|\frac{5}{30120}|\times 100^{2}$$

Reduce the fraction \frac{5}{30120} to lowest terms by extracting and canceling out 5.

$$|\frac{1}{6024}|\times 100^{2}$$

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}{6024} is \frac{1}{6024}.

$$\frac{1}{6024}\times 100^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$\frac{1}{6024}\times 10000$$

Multiply \frac{1}{6024} and 10000 to get \frac{1250}{753}.

$$\frac{1250}{753}$$

Factor

$$\frac{2 \cdot 5 ^ {4}}{3 \cdot 251} = 1\frac{497}{753} = 1.6600265604249669$$