Question

Lara has her baby weighed at an early childhood centre every four weeks. The uncertainty in the measurement is $50\text{g}$. When the baby gets four weeks old, its weight is measured as $3.20\text{kg}$. When he gets eight weeks old, its weight is measured as $4.05\text{kg}$. The baby's weight gain in this four week period is therefore:

• A. $0.85\text{kg}\pm 0.025\text{kg}$
• B. $0.85\text{kg}\pm 0.05\text{kg}$
• C. $0.85\text{kg}\pm 0.1\text{kg}$
• D. $0.8\text{kg}\pm 0.1\text{kg}$

Answer 1

The correct option is D $0.8\text{kg}\pm 0.1\text{kg}$

The weight gain is found by subtracting the first weight from the second. Whenever measurements are added or subtracted the uncertainty in the result is found by summing the uncertainties in the measurements. If the measurements are $X\pm \Delta X$ and $Y\pm \Delta Y$ then where $Z=X-Y,\Delta Z=\Delta X+\Delta Y$. (This is the case when the uncertainties are independent, a more complete analysis requires the adding of squares instead, which in this case gives the same answer). Hence, the uncertainty is $0.1\text{kg}$ in this case. The precision of the result must match that of the uncertainty, in this case only one decimal place, hence the weight gain of $0.85\text{kg}$ is rounded to $0.8\text{kg}$. This gives answer .