sqrt (((0.049)/(54.912))^2+((0.020)/(1.00))^2+((2times 0.036)/(5.09))^2)

To solve the given expression, we need to calculate the square root of the sum of the squares of the fractions.<br /><br />Let's break down the expression step by step:<br /><br />1. Calculate the numerator and denominator of each fraction separately:<br /> - $\frac{0.049}{54.912}$<br /> - $\frac{0.020}{1.00}$<br /> - $\frac{2 \times 0.036}{5.09}$<br /><br />2. Square each fraction:<br /> - $(\frac{0.049}{54.912})^2$<br /> - $(\frac{0.020}{1.00})^2$<br /> - $(\frac{2 \times 0.036}{5.09})^2$<br /><br />3. Add the squared fractions together:<br /> - $(\frac{0.049}{54.912})^2 + (\frac{0.020})^2 + (\frac{2 \times 0.036}{5.09})^2$<br /><br />4. Finally, take the square root of the sum:<br /> - $\sqrt{(\frac{0.049}{54.912})^2 + (\frac{0.020}{1.00})^2 + (\frac{2 \times 0.036}{5.09})^2}$<br /><br />Now, let's calculate the values:<br /><br />1. $\frac{0.049}{54.912} \approx 0.000888$<br />2. $\frac{0.020}{1.00} = 0.020$<br />3. $\frac{2 \times 0.036}{5.09} \approx 0.0142$<br /><br />Squaring these values:<br /><br />1. $(0.000888)^2 \approx 0.000000789$<br />)^2 = 0.0004$<br />3. $(0.0142)^2 \approx 0.00020164$<br /><br />Adding these squared values:<br /><br />$0.000000789 + 0.0004 + 0.00020164 \approx 0.000602429$<br /><br />Finally, taking the square root:<br /><br />$\sqrt{0.000602429} \approx 0.0245$<br /><br />Therefore, the value of the given expression is approximately 0.0245.