(Solved): Significant Figures: Perform the following calculations to the correct number of significant figure ...

Significant Figures: Perform the following calculations to the correct number of significant figures. 1. \( \pi(6.0 \mathrm{~cm})^{2}= \) 2. \( 23.2 \mathrm{~cm}+5.174 \mathrm{~cm}= \) 3. \( 1.0001 m+0.0003 m= \) 4. \( 1.002 m-0.998 m= \) 5. A carpet is to be installed in a rectangular room whose length is measured to be \( 12.71 \mathrm{~m} \) and Whose width is measured to be \( 3.46 \mathrm{~m} \). Find the area of the room. 6. The speed of light is now defined to be \( 2.99792458 \times 10^{1} \mathrm{~m} / \mathrm{s} \). Express the speed of light to (a) three significant figures, (b) five significant figures, and (c) seven significant figures. 7. Using your calculator, determine the following : ("put your answer in scientific notation with appropriate rounding to the correct number of significant figures) a) \( \left(2.437 \times 10^{4}\right)\left(6.5211 \times 10^{5}\right) /\left(5.37 \times 10^{4}\right) \) b) \( \left(3.14159 \times 10^{2}\right)\left(2.701 \times 10^{5}\right) /\left(1.234 \times 10^{9}\right) \)