Question

part a
you have used 290 l of distilled water for a dialysis patient. how many gallons of water is that?
express your answer to two significant figures.
part b
a patient needs 0.024 g of a sulfa drug. there are 6-mg tablets in stock. how many tablets should be given?
express your answer to one significant figure.

Explanation:

Part A

Step1: Recall the conversion factor

We know that \( 1 \, \text{L} \approx 0.264172 \, \text{gal} \).

Step2: Multiply the volume in liters by the conversion factor

To find the volume in gallons, we multiply the given volume in liters (290 L) by the conversion factor. So, \( 290 \, \text{L} \times 0.264172 \, \frac{\text{gal}}{\text{L}} \).

Step3: Calculate the result and round to two significant figures

First, calculate the product: \( 290\times0.264172 = 76.60988 \, \text{gal} \). Rounding to two significant figures, we look at the first two significant digits (7 and 6) and the next digit (6) which is greater than 5, so we round up the second digit. Thus, \( 77 \, \text{gal} \) (or in more precise rounding, since 290 has two significant figures? Wait, 290 - if it's two significant figures, the trailing zero is not significant. Wait, actually, 290 could be considered as two or three significant figures. But the problem says "express your answer to two significant figures". Let's recalculate: \( 290\times0.264172 = 76.60988 \). Rounding to two significant figures: the first two are 7 and 6, the next digit is 6, so we round 76.60988 to 77 (since 76.60988 is closer to 77 when rounding to two significant figures? Wait, no: 76.60988, the first two significant figures are 7 and 6 (7.6 x 10^1), and the next digit is 6, which is more than 5, so we round the 6 up to 7, so 7.7 x 10^1, which is 77. Wait, but actually, 290 L - if 290 is two significant figures (the zero is a placeholder), then 2.9 x 10^2 L. Then 2.9 x 10^2 L 0.264172 gal/L = 2.9 0.264172 x 10^2 gal = 0.7661988 x 10^2 gal = 76.61988 gal, which rounds to 77 gal (two significant figures).

Step1: Convert grams to milligrams

We know that \( 1 \, \text{g} = 1000 \, \text{mg} \), so \( 0.024 \, \text{g} = 0.024\times1000 \, \text{mg} = 24 \, \text{mg} \).

Step2: Calculate the number of tablets

Each tablet is 6 mg, so the number of tablets \( n = \frac{24 \, \text{mg}}{6 \, \text{mg/tablet}} \).

Step3: Calculate the result and round to one significant figure

\( \frac{24}{6} = 4 \). Rounding to one significant figure, 4 is already one significant figure? Wait, 0.024 g has two significant figures, but the problem says to express the answer to one significant figure. Wait, 24 mg divided by 6 mg/tablet is 4. Rounding 4 to one significant figure is 4? Wait, no: 4 is one significant figure? Wait, 4 has one significant figure. Wait, but let's check: 0.024 g is 24 mg (two significant figures), but the problem says to express the answer to one significant figure. So 4 rounded to one significant figure is 4? Wait, no, 4 is one significant figure. Wait, maybe I made a mistake. Wait, 0.024 g is 2.4 x 10^1 mg (two significant figures). Then dividing by 6 mg/tablet (one significant figure? Wait, 6 -mg tablets: is 6 one or two significant figures? If 6 is one significant figure, then 2.4 x 10^1 mg / 6 mg/tablet = 4 (but 6 is one significant figure, so the result should be one significant figure). Wait, 2.4 x 10^1 / 6 = 4, which is 4.0 if we consider, but rounding to one significant figure, 4 is 4 (since 4 is between 1 and 10, one significant figure). Wait, maybe the problem considers 6 mg as one significant figure (the 6), so 0.024 g is 24 mg (two significant figures), but we need to round the answer to one significant figure. So 24 / 6 = 4, which is 4 (one significant figure).

Answer:

\( 77 \) (or more accurately, if we consider 290 as three significant figures, but the problem says two, so 77)

Part B