1. Write $9.02 \times 10^{5}$ as an ordinary number. To convert from standard form, multiply 9.02 by $10^{5} = 100000$. $$9.02 \times 100000 = 902000$$ So the ordinary number is 902000. 2. Work out the value of angle $r$ in the irregular hexagon with alternating angles 131° and $r$. The sum of interior angles of a hexagon is $(6-2) \times 180 = 720$ degrees. There are three angles each of 131°, and three angles each of $r$. Sum of all angles: $$3 \times 131 + 3 \times r = 720$$ Calculate: $$393 + 3r = 720$$ Subtract 393 from both sides: $$3r = 720 - 393 = 327$$ Divide both sides by 3: $$r = \frac{327}{3} = 109$$ degrees. 3. Convert $6.035 \times 10^{-4}$ to an ordinary number. $10^{-4} = 0.0001$ Multiply: $$6.035 \times 0.0001 = 0.0006035$$ So the ordinary number is 0.0006035. 4. Lucas's mistake writing 2300 as $23 \times 10^{2}$. a) Explanation: Lucas incorrectly moved the decimal one place to the left to get 23 instead of two places to get 2.3. The standard form requires a number between 1 and 10. b) Correct answer: $$2300 = 2.3 \times 10^{3}$$ 5. Write 0.00316 in standard form. Move the decimal 3 places to the right to get 3.16: $$0.00316 = 3.16 \times 10^{-3}$$ 6. Work out the size of angle $p$ in the triangle sharing a side with a pentagon. Sum of triangle angles is 180°. Given angles: 61° and $p$, unknown third angle. The pentagon angles are 78°, 108°, 22°, and 113°, but those do not affect triangle angles here directly. To find the third angle of the triangle, observe the shared side with the pentagon and check angles at common vertices. The unknown adjacent angle is calculated by supplementing pentagon angles. However, as per the figure: Angles in triangle: 61°, $p$, and adjacent to 78°. The angle adjacent to 78° and inside the triangle is supplementary to 78°, so: Third angle in triangle = 180 - 78 = 102°. Sum of triangle angles: $$61 + p + 102 = 180$$ Simplify: $$163 + p = 180$$ Subtract 163: $$p = 17$$ degrees. 7. Convert 52900 to standard form. Move decimal 4 places to the left: $$52900 = 5.29 \times 10^{4}$$ 8. Convert 0.00068 to standard form. Move decimal 4 places to the right: $$0.00068 = 6.8 \times 10^{-4}$$ 9. Write 4070 in standard form. Move decimal 3 places to the left: $$4070 = 4.07 \times 10^{3}$$