Calculating Upper and Lower Bounds of Chemical Mass
The image contains the following question:
"At the start of an experiment, some chemicals had a mass of 62 g, rounded to 2 significant figures.
During the experiment, the mass of the chemicals decreased by 7.3 g, rounded to 2 significant figures.
Calculate the lower and upper bounds of the mass of the chemicals at the end of the experiment."
To solve this, we need to calculate the upper and lower bounds considering the number of significant figures the values were rounded to.
For the starting mass 62 g rounded to 2 significant figures, the lower bound would be one half unit of the last significant digit less than 62 g, and the upper bound would be one half unit of the last significant digit more than 62 g. Since the last significant digit is in the tens place, a half unit is 0.5 tens, which is 5 g.
Lower bound of the starting mass = 62 g - 5 g = 57 g
Upper bound of the starting mass = 62 g + 5 g = 67 g
For the decrease in mass 7.3 g rounded to 2 significant figures, the last significant figure is in the tenths place, so one half of the last significant digit is 0.05 g.
Lower bound of the decrease in mass = 7.3 g - 0.05 g = 7.25 g
Upper bound of the decrease in mass = 7.3 g + 0.05 g = 7.35 g
To find the bounds of the mass of the chemicals at the end of the experiment, subtract the calculated decrease bounds from the calculated mass bounds:
Lower bound at end = Lower bound of starting mass - Upper bound of decrease in mass
Upper bound at end = Upper bound of starting mass - Lower bound of decrease in mass
Lower bound at end = 57 g - 7.35 g = 49.65 g
Upper bound at end = 67 g - 7.25 g = 59.75 g
So, the lower and upper bounds of the mass of the chemicals at the end of the experiment are 49.65 g and 59.75 g, respectively.
