Solve 0.9/3sqrt{3/2*10^8}

$$\frac{ 0.9 }{ \frac{ 3 \sqrt{ 3 } }{ 2 } \times { 10 }^{ 8 } }$$

Evaluate

$$\frac{\sqrt{3}}{500000000}\approx 3.464101615 \cdot 10^{-9}$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\frac{0.9}{\frac{3\sqrt{3}}{2}\times 100000000}$$

Cancel out 2, the greatest common factor in 100000000 and 2.

$$\frac{0.9}{50000000\times 3\sqrt{3}}$$

Rationalize the denominator of \frac{0.9}{50000000\times 3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{0.9\sqrt{3}}{50000000\times 3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{0.9\sqrt{3}}{50000000\times 3\times 3}$$

Multiply 50000000 and 3 to get 150000000.

$$\frac{0.9\sqrt{3}}{150000000\times 3}$$

Multiply 150000000 and 3 to get 450000000.

$$\frac{0.9\sqrt{3}}{450000000}$$

Divide 0.9\sqrt{3} by 450000000 to get 0.000000002\sqrt{3}.

$$0.000000002\sqrt{3}$$