Problem 80 - Chemistry Matter and Change

Question

Convert the following measurements. \(\begin{array}{ll}{\text { a. } 5.70 \mathrm{g} \text { to milligrams }} & {\text { d. } 45.3 \mathrm{mm} \text { to meters }} \\ {\text { b. } 4.37 \mathrm{cm} \text { to meters }} & {\text { e. } 10 \mathrm{m} \text { to centimeters }} \\ {\text { c. } 783 \mathrm{kg} \text { to grams }} & {\text { f. } 37.5 \mathrm{g} / \mathrm{mL} \text { to } \mathrm{kg} / \mathrm{L}}\end{array}\)

Step-by-Step Solution

Answer

a. 5700 mg b. 0.0437 m c. 783,000 g d. 0.0453 m e. 1000 cm f. 37.5 kg/L

Step 1: a. 5.70 g to milligrams

To convert grams (g) to milligrams (mg), we need to know the conversion factor: 1 gram = 1000 milligrams So, for 5.70g: \(5.70g * \frac{1000mg}{1g} = 5700mg\)

Step 2: b. 4.37 cm to meters

To convert centimeters (cm) to meters (m), we need to know the conversion factor: 1 centimeter = 0.01 meters So, for 4.37 cm: \(4.37cm * \frac{0.01m}{1cm} = 0.0437m\)

Step 3: c. 783 kg to grams

To convert kilograms (kg) to grams (g), we need to know the conversion factor: 1 kilogram = 1000 grams So, for 783 kg: \(783kg * \frac{1000g}{1kg} = 783,000g\)

Step 4: d. 45.3 mm to meters

To convert millimeters (mm) to meters (m), we need to know the conversion factor: 1 millimeter = 0.001 meters So, for 45.3 mm: \(45.3mm * \frac{0.001m}{1mm} = 0.0453m\)

Step 5: e. 10 m to centimeters

To convert meters (m) to centimeters (cm), we need to know the conversion factor: 1 meter = 100 centimeters So, for 10 m: \(10m * \frac{100cm}{1m} = 1000cm\)

Step 6: f. 37.5 g/mL to kg/L

To convert from grams per milliliter (g/mL) to kilograms per liter (kg/L), we need to know the conversion factors for both mass and volume: 1 gram = 0.001 kilograms 1 liter = 1000 milliliters So, for 37.5 g/mL: \(37.5\frac{g}{mL} * \frac{0.001kg}{1g} * \frac{1000mL}{1L} = 37.5\frac{kg}{L}\)

Key Concepts

Understanding Measurement Conversions

Measurement conversions are a fundamental part of mathematics and science, helping us to express quantities in different units, making it simpler to solve problems and conduct experiments. Understanding these conversions is like having a key that unlocks smooth progression in calculations involving different units. Measurement conversions involve using conversion factors to change a quantity expressed in one unit into another. For example, to convert grams to milligrams, we use the conversion factor that 1 gram equals 1000 milligrams. This enables you to multiply the number of grams by 1000 to get the equivalent number of milligrams.

• Conversion factors act as a bridge between units.
• It's crucial to align the units appropriately to ensure correct conversion.
• Converting between units helps in understanding and interpreting data correctly across various applications.

Remembering these conversion factors and applying them correctly aids in effective problem-solving within many scientific and mathematical fields.

Exploring the Metric System

The metric system is the international standard for measurement and is used almost universally across the globe. It is a decimal-based system that makes it easy to convert between units, as you often just need to shift the decimal point. In the metric system:

• The fundamental units are meters for length, grams for mass, and liters for volume.
• The system uses prefixes like kilo-, centi-, and milli- to denote multiples or fractions of these base units.
• For instance, a kilometer is 1000 meters, a centimeter is 0.01 meters, and a milligram is 0.001 grams.

This systematic approach makes calculations simpler, as each step is a multiple of ten, which is easy to handle for computations in everyday situations and complex scientific calculations alike. Working within the metric system can streamline learning and working with numbers and measurements.

Mass Conversion Techniques

Mass conversion is a tool that allows us to interchange units of mass like kilograms, grams, and milligrams, which are all part of the metric system. To convert between these units:

• Remember 1 kilogram equals 1000 grams.
• 1 gram equals 1000 milligrams.
• Thus, converting from kilograms to grams or grams to milligrams is simply moving the decimal place three positions.

For example, if you have 783 kilograms and want to express it in grams, multiply by 1000, resulting in 783,000 grams. These techniques become intuitive with practice, allowing for quick mental calculations or accurate written computations.

Mastering Length Conversion

Length conversion is essential for understanding how to measure distances and dimensions in different scenarios. Within the metric system, length units include meters, centimeters, and millimeters. For converting lengths:

• Know that 1 meter equals 100 centimeters.
• And that 1 centimeter is 0.01 meters.
• Additionally, 1 millimeter is 0.001 meters.

Converting 4.37 centimeters to meters involves multiplying by 0.01, resulting in 0.0437 meters. For instance, converting millimeters to meters, multiply by 0.001. This straightforward method ensures clarity whether you're measuring a short length like fabric or a component part for engineering. Length conversion within the metric system is simple and designed for universal understanding.