Use the following chart to do the conversion of grains to milligrams. Approximate Equivalents: – teaspoon = 5 milliliters – kilogram = 72.2 pounds – grain = 60 milligrams – teaspoon = 60 drops – grain = 1 drop – quart = liter – fluid ounce = 1/6 teaspoons – pint = 2 cups – fluid ounce = 2 tablespoons – quart = 32 fluid ounces – fluid ounce = 30 milliliters – gram = 15 grains – inch = 2.54 centimeters – cup = 240 milliliters The answer is milligrams: (Type an integer or decimal rounded to the nearest tenth as needed) The answer is grams: (Type an integer or decimal rounded to the nearest hundredth as needed)
The Correct Answer and Explanation is:
To solve this problem, we’ll use the conversion factors given in the chart:
- 1 grain = 60 milligrams
- 1 gram = 15 grains
We are not provided with a specific number of grains in the question, but from the structure of the prompt and the matching conversion chart, we can deduce that we are to convert 1 grain into milligrams and grams.
Step 1: Convert grains to milligrams
Using the equivalence:
1 grain=60 milligrams1 \text{ grain} = 60 \text{ milligrams}
So, the answer is 60.0 milligrams (rounded to the nearest tenth).
Step 2: Convert grains to grams
Since 1 gram = 15 grains, we divide:
1 grain=115 grams=0.0667 grams1 \text{ grain} = \frac{1}{15} \text{ grams} = 0.0667 \text{ grams}
Rounding to the nearest hundredth gives 0.07 grams.
Explanation
Converting between units involves using known equivalences to translate a quantity from one unit to another. In this case, we are converting from grains, a unit of mass historically used in pharmacy and medicine, to milligrams and then to grams, which are metric units of mass more commonly used in scientific and health-related fields.
The chart indicates that 1 grain equals 60 milligrams. This allows for a straightforward multiplication. If we were converting multiple grains, we would multiply the number of grains by 60 to get the number of milligrams. Here, since we’re working with 1 grain, it equals exactly 60 milligrams. Rounding this to the nearest tenth still gives 60.0.
To express grains in grams, we use the equivalence that 1 gram equals 15 grains. By taking the reciprocal, we find that 1 grain equals 1 divided by 15 grams. This division yields approximately 0.0667 grams. Since the instructions ask for rounding to the nearest hundredth, the answer becomes 0.07 grams.
These conversions are useful in various applications. For instance, medication dosages may be prescribed in grains or milligrams depending on the region or medical tradition. Understanding how to move between these units ensures accurate dosing and safe practices in health care.
The logic used here demonstrates a typical approach in scientific measurement problems: identify a reliable conversion factor and apply basic arithmetic operations. This method applies broadly, whether converting between fluid volumes, weights, or distances.
