Problem 19 - Chemistry for Allied Health

Question

Complete each of the following conversions. a. \(34 \mathrm{~cm}\) to \(\mathrm{m}\) b. \(3.7 \mathrm{ft}\) to in c. \(345 \mathrm{mg}\) to \(\mathrm{Mg}\) d. \(5.3 \mathrm{~km}\) to \(\mathrm{mm}\) e. \(4.0 \mathrm{~L}\) to \(\mathrm{mL}\) f. \(3.45 \times 10^{3} \mathrm{~mm}\) to \(\mathrm{km}\) g. \(78 \mathrm{~cm}^{3}\) to \(\mathrm{mL}\) h. \(0.85 \mathrm{~kg}\) to \(\mathrm{dg}\) i. 13 pints to gallon j. \(0.35 \mathrm{~L}\) to \(\mathrm{cm}^{3}\)

Step-by-Step Solution

Answer

a. 0.34 m; b. 44.4 in; c. 3.45 × 10⁻⁷ Mg; d. 5,300,000 mm; e. 4,000 mL; f. 3.45 × 10⁻³ km; g. 78 mL; h. 8,500 dg; i. 1.625 gal; j. 350 cm³.

Step 1: Convert cm to m

To convert centimeters to meters, divide the number by 100, since 1 meter = 100 centimeters. \[34\, \text{cm} \times \frac{1\, \text{m}}{100\, \text{cm}} = 0.34\, \text{m}\]

Step 2: Convert ft to in

To convert feet to inches, multiply by 12, since 1 foot = 12 inches.\[3.7\, \text{ft} \times 12\, \text{in/ft} = 44.4\, \text{in}\]

Step 3: Convert mg to Mg

To convert milligrams to megagrams, divide the number by 1,000,000,000 because 1 Mg = 1,000,000,000 mg.\[345\, \text{mg} \times \frac{1\, \text{Mg}}{1,000,000,000\, \text{mg}} = 3.45 \times 10^{-7}\, \text{Mg}\]

Step 4: Convert km to mm

To convert kilometers to millimeters, multiply by 1,000,000 since 1 km = 1,000,000 mm.\[5.3\, \text{km} \times 1,000,000\, \text{mm/km} = 5,300,000\, \text{mm}\]

Step 5: Convert L to mL

To convert liters to milliliters, multiply by 1,000 since 1 L = 1,000 mL.\[4.0\, \text{L} \times 1,000\, \text{mL/L} = 4,000\, \text{mL}\]

Step 6: Convert mm to km

To convert millimeters to kilometers, divide by 1,000,000 since 1 km = 1,000,000 mm.\[3.45 \times 10^{3}\, \text{mm} \times \frac{1\, \text{km}}{1,000,000\, \text{mm}} = 3.45 \times 10^{-3}\, \text{km}\]

Step 7: Convert cm³ to mL

1 cm³ is equivalent to 1 mL.\[78\, \text{cm}^3 = 78\, \text{mL}\]

Step 8: Convert kg to dg

To convert kilograms to decigrams, multiply by 10,000 since 1 kg = 10,000 dg.\[0.85\, \text{kg} \times 10,000\, \text{dg/kg} = 8,500\, \text{dg}\]

Step 9: Convert pints to gallons

To convert pints to gallons, divide by 8, since 1 gallon = 8 pints.\[13\, \text{pt} \times \frac{1\, \text{gal}}{8\, \text{pt}} = 1.625\, \text{gal}\]

Step 10: Convert L to cm³

1 L is equivalent to 1000 cm³.\[0.35\, \text{L} \times 1,000\, \text{cm}^3/\text{L} = 350\, \text{cm}^3\]

Key Concepts

Metric Conversions

The metric system is a universal language of measurement, and understanding how to convert between its units is a handy skill. In metric conversions, we typically move the decimal point to convert units like centimeters to meters or liters to milliliters. The key is knowing the base units:

• 1 meter = 100 centimeters
• 1 kilometer = 1,000 meters
• 1 liter = 1,000 milliliters
• 1 kilogram = 1,000 grams

Each conversion is based on factors of ten, making it straightforward. For example, to convert 34 centimeters to meters, divide by 100, because 100 cm equals 1 m. Therefore, 34 cm is 0.34 m. This simplicity is what makes metric conversions extremely efficient.

Volume Conversion

Volume conversion is all about knowing how different units of volume relate to each other. Many times, volume is measured in liters, milliliters, or cubic centimeters (cm³). A core understanding here is:

• 1 liter = 1,000 milliliters
• 1 cm³ = 1 milliliter

If you have a measurement in liters and need it in milliliters, like converting 4 liters to milliliters, simply multiply by 1,000 to get 4,000 mL. This is because a liter has 1,000 smaller units within it. Volume conversion might also involve other units such as gallons or pints, commonly used in the US. For those, knowing the conversion factor is key: for instance, 1 gallon equals 8 pints. Thus, converting across different volume units requires a quick multiplication or division based on these established relationships.

Length Conversion

Length is one of the most commonly measured quantities. Whether it’s converting feet to inches or kilometers to millimeters, it involves knowing the relationship between the units:

• 1 foot = 12 inches
• 1 km = 1,000,000 mm
• 1 meter = 100 centimeters

To convert 3.7 feet to inches, multiply by 12 to yield 44.4 inches. For longer distances, such as kilometers to millimeters, multiply by 1,000,000. These conversions allow you to go from small units like millimeters, suitable for minute measurements, to larger units like kilometers for distance. Each conversion simply requires either moving the decimal (for metrics) or using a specific factor (like ft to in, or pints to gallons), always keeping the unit’s conversion rule in mind.

Mass Conversion

Mass conversion lets us understand how weight scales across different units, primarily in the metric system. The fundamental units include grams, kilograms, and milligrams, with conversions often being straightforward due to the base-ten structure.

• 1 kilogram = 1,000 grams
• 1 megagram = 1,000,000 grams
• 1 milligram = 0.001 grams

For example, converting 345 mg to Mg (megagrams) involves dividing by 1,000,000,000, since 1 Mg is 1 billion milligrams. Similarly, when converting kilograms to decigrams, multiply by 10,000, since a kilogram contains 10,000 decigrams. Mastering these conversions helps in weighing and comparing masses in science, cooking, or any situation requiring precision.