Solve 1/0.05^2:1/0.20^2:1/0.10^2

$$\frac { 1 } { 0.05 ^ { 2 } } : \frac { 1 } { 0.20 ^ { 2 } } : \frac { 1 } { 0.10 ^ { 2 } }$$

Evaluate

$$0.16$$

Solution Steps

Divide \frac{\frac{1}{0.05^{2}}}{\frac{1}{0.2^{2}}} by \frac{1}{0.1^{2}} by multiplying \frac{\frac{1}{0.05^{2}}}{\frac{1}{0.2^{2}}} by the reciprocal of \frac{1}{0.1^{2}}.

$$\frac{\frac{1}{0.05^{2}}\times 0.1^{2}}{\frac{1}{0.2^{2}}}$$

Calculate 0.05 to the power of 2 and get 0.0025.

$$\frac{\frac{1}{0.0025}\times 0.1^{2}}{\frac{1}{0.2^{2}}}$$

Expand \frac{1}{0.0025} by multiplying both numerator and the denominator by 10000.

$$\frac{\frac{10000}{25}\times 0.1^{2}}{\frac{1}{0.2^{2}}}$$

Divide 10000 by 25 to get 400.

$$\frac{400\times 0.1^{2}}{\frac{1}{0.2^{2}}}$$

Calculate 0.1 to the power of 2 and get 0.01.

$$\frac{400\times 0.01}{\frac{1}{0.2^{2}}}$$

Multiply 400 and 0.01 to get 4.

$$\frac{4}{\frac{1}{0.2^{2}}}$$

Calculate 0.2 to the power of 2 and get 0.04.

$$\frac{4}{\frac{1}{0.04}}$$

Expand \frac{1}{0.04} by multiplying both numerator and the denominator by 100.

$$\frac{4}{\frac{100}{4}}$$

Divide 100 by 4 to get 25.

$$\frac{4}{25}$$

Factor

$$\frac{2 ^ {2}}{5 ^ {2}} = 0.16$$