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To obtain 4 liters using 3-liter and 5-liter jugs, we want to reach the point (4, 0). From the point (4, 0), there are only two reversible actions: filling the empty 3-liter jug to full from the tap (4,3), or transferring 1 liter of water from the 5-liter jug to the 3-liter jug (1,3). Therefore, there are only two solutions to the problem:
To create the solution, 11.6 g NaCl is placed in a volumetric flask, dissolved in some water, then followed by the addition of more water until the total volume reaches 100 mL. The density of water is approximately 1000 g/L and its molar mass is 18.02 g/mol (or 1/18.02 = 0.055 mol/g). Therefore, the molar concentration of water is
Percentage solution may refer to: Mass fraction (or "% w/w" or "wt.%"), for percent mass; Volume fraction (or "% v/v" or "vol.%"), volume concentration, for percent volume "Mass/volume percentage" (or "% m/v") in biology, for mass per unit volume; incorrectly used to denote mass concentration (chemistry). See usage in biology
This improper name persists, especially in elementary textbooks. In biology, the unit "%" is sometimes (incorrectly) used to denote mass concentration, also called mass/volume percentage. A solution with 1 g of solute dissolved in a final volume of 100 mL of solution would be labeled as "1%" or "1% m/v" (mass/volume). This is incorrect because ...
For example, to make 100 mL of 50% alc/vol ethanol solution, water would be added to 50 mL of ethanol to make up exactly 100 mL. Whereas to make a 50% v/v ethanol solution, 50 mL of ethanol and 50 mL of water could be mixed but the resulting volume of solution will measure less than 100 mL due to the change of volume on mixing, and will contain ...
For instance, a change in an interest rate from 5.15% per annum to 5.35% per annum could be denoted as a change of 20 basis points (per annum). As with interest rates, the words "per annum" (or "per year") are often omitted. In that case, the basis point is a quantity with a dimension of (time −1). [2]
The concentration of alcohol in a beverage is usually stated as the percentage of alcohol by volume (ABV, the number of milliliters (ml) of pure ethanol in 100 ml of beverage) or as proof. In the United States , proof is twice the percentage of alcohol by volume at 60 degrees Fahrenheit (e.g. 80 proof = 40% ABV).
In general, if an increase of x percent is followed by a decrease of x percent, and the initial amount was p, the final amount is p (1 + 0.01 x)(1 − 0.01 x) = p (1 − (0.01 x) 2); hence the net change is an overall decrease by x percent of x percent (the square of the original percent change when expressed as a decimal number).