Question: A student works out an estimate for this calculation. $$\frac{13.7 + 1.28}{5.099}$$ Their method is to: • round each number correct to the same number of significant figures and • work out the approximation. The student writes $$\frac{14 + 1}{5} = \frac{15}{3}$$ What error has the student made in using their method?

1. **State the problem:** We want to estimate the value of $$\frac{13.7 + 1.28}{5.099}$$ by rounding each number to the same number of significant figures and then calculating the approximation. 2. **Student's rounding:** - Rounded $$13.7$$ to $$14$$ (2 significant figures). - Rounded $$1.28$$ to $$1$$ (1 significant figure). - Rounded $$5.099$$ to $$5$$ (1 significant figure). 3. **Student's calculation:** They added the rounded numerator: $$14 + 1 = 15$$. Then they wrote the denominator as $$3$$ instead of $$5$$, which is incorrect. 4. **Error analysis:** The student incorrectly changed the denominator from $$5$$ to $$3$$ without justification. Also, the student rounded $$1.28$$ to $$1$$, which is inconsistent with rounding $$13.7$$ to $$14$$ (2 significant figures vs 1 significant figure). 5. **Correct rounding:** - Round $$13.7$$ and $$1.28$$ both to 2 significant figures: - $$13.7 \to 14$$ - $$1.28 \to 1.3$$ - Round denominator $$5.099$$ to 3 significant figures: - $$5.099 \to 5.10$$ 6. **Correct approximate calculation:** $$\frac{14 + 1.3}{5.10} = \frac{15.3}{5.10} \approx 3$$ 7. **Summary:** The student's error was: - Rounding numbers to different numbers of significant figures inconsistently. - Incorrectly changing the denominator value from $$5$$ to $$3$$. This leads to an incorrect approximation. **Final answer:** The student incorrectly changed the denominator from $$5$$ to $$3$$ and rounded numbers inconsistently, causing an error in the approximation.