1. Evaluate i) $\frac{1}{4} \times 10^{-5}$. Recall that $10^{-5} = \frac{1}{10^5} = \frac{1}{100000}$. So, $$\frac{1}{4} \times 10^{-5} = \frac{1}{4} \times \frac{1}{100000} = \frac{1}{400000} = 2.5 \times 10^{-6}.$$ 2. Evaluate ii) $\sqrt{\frac{1}{25}}$. Since $\frac{1}{25} = \left(\frac{1}{5}\right)^2$, the square root is: $$\sqrt{\frac{1}{25}} = \frac{1}{5} = 0.2.$$ 3. Simplify the expression: $$(-3)^{-2} - (-1)^0 + 1^{-2} - \frac{1}{9}$$ Step-by-step: - $(-3)^{-2} = \frac{1}{(-3)^2} = \frac{1}{9}$. - $(-1)^0 = 1$ because any nonzero number raised to the zero power is 1. - $1^{-2} = \frac{1}{1^2} = 1$. - $\frac{1}{9}$ remains unchanged. So, the expression equals: $$\frac{1}{9} - 1 + 1 - \frac{1}{9} = \left(\frac{1}{9} - \frac{1}{9}\right) + (1 - 1) = 0 + 0 = 0.$$ Therefore, the expression equals $0$, not $1$ as originally stated. 4. Numerical sense question: Is $\sqrt{0.0}$ equal to 0.005? By definition, $\sqrt{0.0} = 0.0$, since the square root of zero is zero. Therefore, $\sqrt{0.0}$ is not 0.005; it is exactly $0$.