1. **State the problem:** We have 10 boys and 20 girls in a class. The mean mark for the whole class is 60, and the mean mark for the girls is 54. We need to find the mean mark for the boys. 2. **Formula and rules:** The mean mark for the whole class is the total marks divided by the total number of students. Let $M_b$ be the mean mark for the boys. Total students = 10 boys + 20 girls = 30 students. Total marks for the class = mean $ \times $ number of students = $60 \times 30 = 1800$. Total marks for the girls = mean $ \times $ number of girls = $54 \times 20 = 1080$. 3. **Calculate total marks for boys:** $$\text{Total marks for boys} = \text{Total marks for class} - \text{Total marks for girls} = 1800 - 1080 = 720$$ 4. **Calculate mean mark for boys:** $$M_b = \frac{\text{Total marks for boys}}{\text{Number of boys}} = \frac{720}{10}$$ 5. **Simplify the fraction:** $$M_b = \frac{\cancel{720}}{\cancel{10}} = 72$$ **Final answer:** The mean mark for the boys is **72**. --- 6. **Next problem (8a):** Write $7.97 \times 10^{-6}$ as an ordinary number. Move the decimal point 6 places to the left because the exponent is negative: $$7.97 \times 10^{-6} = 0.00000797$$ --- 7. **Next problem (8b):** Calculate $\frac{2.52 \times 10^{5}}{4 \times 10^{-3}}$ and give the answer in standard form. Use the rule for division of numbers in standard form: $$\frac{a \times 10^{m}}{b \times 10^{n}} = \frac{a}{b} \times 10^{m-n}$$ Calculate the coefficient: $$\frac{2.52}{4} = 0.63$$ Calculate the power of 10: $$10^{5 - (-3)} = 10^{5 + 3} = 10^{8}$$ So, $$\frac{2.52 \times 10^{5}}{4 \times 10^{-3}} = 0.63 \times 10^{8}$$ Rewrite $0.63 \times 10^{8}$ in standard form: $$0.63 \times 10^{8} = 6.3 \times 10^{7}$$ **Final answer:** $6.3 \times 10^{7}$