DO NOT WRITE IN THIS AREA DO NOT WRITE I 1. (a) (i) Calculate the value of \( \sqrt{(7.1)^{2}+(2.9)^{2}} \), giving your answer correct to a) \( \quad 2 \) significant figures (1 mark) b) \( \quad 2 \) decimal places. (1 mark) (ii) Write the following quantities in ascending order. \[ \frac{12}{25}, \quad 0.46, \quad 47 \% \] WRITE IN THIS AREA \( \qquad \) \( \qquad \) \( \qquad \) \[ <. \] \( \qquad \) (1 mark)

Calculate the value by following steps: - step0: Calculate: \(\sqrt{7.1^{2}+2.9^{2}}\) - step1: Convert the expressions: \(\sqrt{\left(\frac{71}{10}\right)^{2}+2.9^{2}}\) - step2: Convert the expressions: \(\sqrt{\left(\frac{71}{10}\right)^{2}+\left(\frac{29}{10}\right)^{2}}\) - step3: Add the numbers: \(\sqrt{\frac{2941}{50}}\) - step4: Use the properties of radicals: \(\frac{\sqrt{2941}}{\sqrt{50}}\) - step5: Simplify the expression: \(\frac{\sqrt{2941}}{5\sqrt{2}}\) - step6: Multiply by the Conjugate: \(\frac{\sqrt{2941}\times \sqrt{2}}{5\sqrt{2}\times \sqrt{2}}\) - step7: Multiply the numbers: \(\frac{\sqrt{5882}}{5\sqrt{2}\times \sqrt{2}}\) - step8: Multiply the numbers: \(\frac{\sqrt{5882}}{10}\) Calculate or simplify the expression \( \sqrt((7.1)^2 + (2.9)^2) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{7.1^{2}+2.9^{2}}\) - step1: Convert the expressions: \(\sqrt{\left(\frac{71}{10}\right)^{2}+2.9^{2}}\) - step2: Convert the expressions: \(\sqrt{\left(\frac{71}{10}\right)^{2}+\left(\frac{29}{10}\right)^{2}}\) - step3: Add the numbers: \(\sqrt{\frac{2941}{50}}\) - step4: Use the properties of radicals: \(\frac{\sqrt{2941}}{\sqrt{50}}\) - step5: Simplify the expression: \(\frac{\sqrt{2941}}{5\sqrt{2}}\) - step6: Multiply by the Conjugate: \(\frac{\sqrt{2941}\times \sqrt{2}}{5\sqrt{2}\times \sqrt{2}}\) - step7: Multiply the numbers: \(\frac{\sqrt{5882}}{5\sqrt{2}\times \sqrt{2}}\) - step8: Multiply the numbers: \(\frac{\sqrt{5882}}{10}\) Calculate or simplify the expression \( 12/25 \). Calculate the value by following steps: - step0: Calculate: \(\frac{12}{25}\) Calculate or simplify the expression \( 47/100 \). Calculate the value by following steps: - step0: Calculate: \(\frac{47}{100}\) 1. (a) (i) To calculate \( \sqrt{(7.1)^{2}+(2.9)^{2}} \): First, we compute the expression: \[ \sqrt{(7.1)^{2}+(2.9)^{2}} = \sqrt{50.41 + 8.41} = \sqrt{58.82} \] Now, we find the approximate value: - a) Correct to 2 significant figures: \( \approx 7.7 \) - b) Correct to 2 decimal places: \( \approx 7.67 \) (ii) To write the quantities in ascending order: - \( \frac{12}{25} = 0.48 \) - \( 0.46 \) - \( 47\% = 0.47 \) Now, we can arrange them: \[ 0.46 < 0.47 < 0.48 \] Thus, the final answer is: \[ 0.46 < 47\% < \frac{12}{25} \]