Question

Use metric conversion factors to solve each of the following problems: a. The daily value of phosphorus is \(800 \mathrm{mg}\). How many grams of phosphorus are recommended? b. A glass of orange juice contains \(0.85 \mathrm{dL}\) of juice. How many milliliters of orange juice is that? c. A package of chocolate instant pudding contains \(2840 \mathrm{mg}\) of sodium. How many grams of sodium is that?

Short answer

a. 0.8 gb. 85 mLc. 2.84 g

Step-by-step solution

Convert milligrams to grams (part a)

To convert milligrams to grams, use the conversion factor: 1 gram = 1000 milligrams. Divide 800 mg by 1000. \( \text{Grams of phosphorus} = \frac{800 \text{ mg}}{1000} = 0.8 \text{ g} \).

Convert deciliters to milliliters (part b)

To convert deciliters to milliliters, use the conversion factor: 1 deciliter = 100 milliliters. Multiply 0.85 dL by 100. \( \text{Milliliters of orange juice} = 0.85 \text{ dL} \times 100 = 85 \text{ mL} \).

Convert milligrams to grams (part c)

To convert milligrams to grams, use the conversion factor: 1 gram = 1000 milligrams. Divide 2840 mg by 1000. \( \text{Grams of sodium} = \frac{2840 \text{ mg}}{1000} = 2.84 \text{ g} \).

Key concepts

milligrams to grams conversion

Metric conversions are crucial in chemistry and everyday life, especially with smaller units like milligrams and grams.
To convert milligrams (mg) to grams (g), remember that 1 gram is equal to 1000 milligrams.
So, we use the conversion factor: \[ 1 \text{ g} = 1000 \text{ mg} \].
For example, if you have 800 mg of a substance and want to convert it to grams, you divide it by 1000.
This gives: \[ \text{Grams} = \frac{800 \text{ mg}}{1000} = 0.8 \text{ g} \].
So, 800 mg is 0.8 grams.
This method works for any amount of milligrams you need to convert to grams.

deciliters to milliliters conversion

Understanding conversions between deciliters (dL) and milliliters (mL) is important in measuring liquids.
1 deciliter is equal to 100 milliliters, using the conversion factor: \[ 1 \text{ dL} = 100 \text{ mL} \].
To convert from deciliters to milliliters, you multiply the number of deciliters by 100.
For instance, if you have 0.85 dL of orange juice and want to convert it to milliliters, you would calculate: \[ \text{Milliliters} = 0.85 \text{ dL} \times 100 = 85 \text{ mL} \].
This means that 0.85 dL equals 85 mL.
Deciliters are not as commonly used as milliliters, so knowing this conversion can be very helpful.

unit conversions in chemistry

Unit conversions are foundational in chemistry as they ensure accurate measurements.
Whether calculating doses, reactions, or concentrations, knowing how to convert units accurately is crucial.
Here are some general tips for unit conversions in chemistry:

• Always know the basic conversion factors, like 1 liter = 1000 milliliters.
• Write down the unit you are converting from and to.
• Use the appropriate conversion factor to multiply or divide.
• Double-check your calculations to avoid errors.

For example, let's convert 2840 mg of sodium to grams.
Using the conversion factor \[ 1 \text{ g} = 1000 \text{ mg} \], divide 2840 by 1000: \[ \text{Grams of sodium} = \frac{2840 \text{ mg}}{1000} = 2.84 \text{ g} \].
This ensures precise measurement and consistency in results.