Numbers in Science

In an experiment, a chemist allows a red solution to flow at a rate of 0.1 mL per second for 14 seconds into a beaker containing a blue solution. The red solution has a density of 1.10 g/mL, and the blue solution has a density of 0.98 g/mL. Rounding each answer to the correct number of significant figures, if there are initially 20. mL of blue solution in the beaker:

(a): How many grams of blue solution are in the beaker?
(b): How many milliliters of red solution have been added after 14 seconds?
(c): How many grams of red solution have been added after 14 seconds?
(d): Recalculate the answers for (b) and (c) for a red flow rate of 0.10 mL per second.

Solutions:

(a)  20 g    (b) 1 mL   (c) 2 g   (d) 1.4 mL, 1.5 g

Sketch:

This is largely a problem of unit conversions and keeping track of significant figures. For a flow rate of 0.1 ml per second, there is only 1 significant figure for this measurement, so the answers that use this quantity are only good to 1 significant figure.

(a): 20. mL x .98 g/mL = 19.6 g, but to 2 sig figs, this is rounded to 20. g.
(b): 0.1 mL/s x 14 s = 1.4 mL, so to 1 sig fig this is rounded down to 1 mL.
(c): 0.1 mL/s x 14 s x 1.10 g/mL = 1.54 g, so to 1 sig fig this is rounded up to 2 g.
(d): 0.10 mL/s x 14 s = 1.4 mL, so to 2 sig fig this is 1.4 mL
0.10 mL/s x 14 s x 1.10 g/mL = 1.54 g, so to 2 sig fig this is rounded down to 1.5 g.

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Developed by

Shodor
in cooperation with the Department of Chemistry,
The University of North Carolina at Chapel Hill