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Carry out these conversions: (a) 242 lb to milligrams, (b) \(68.3 \mathrm{~cm}^{3}\) to cubic meters.

Short Answer

Expert verified
(a) 242 lb = 109,772,464 mg, (b) 68.3 cm³ = 0.0000683 m³.

Step by step solution

01

Convert pounds to kilograms

We know from the conversion factor that 1 lb (pound) is equal to 0.453592 kg. Therefore, to convert 242 lb to kg, we use: \[ 242 \text{ lb} \times 0.453592 \text{ kg/lb} = 109.772464 \text{ kg}. \]
02

Convert kilograms to milligrams

Once we have the weight in kilograms, we need to convert it into milligrams. Knowing that 1 kg equals 1,000,000 mg, we calculate: \[ 109.772464 \text{ kg} \times 1,000,000 \text{ mg/kg} = 109,772,464 \text{ mg}. \]
03

Convert cubic centimeters to cubic meters

The conversion factor for cubic centimeters to cubic meters is that 1 \(\text{cm}^3\) is equal to \(1 \times 10^{-6}\) \(\text{m}^3\). So for 68.3 \(\text{cm}^3\), we have: \[ 68.3 \times 10^{-6} = 0.0000683 \text{ m}^3. \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mass Conversion
Converting mass, like changing pounds to milligrams, involves understanding different units of measurement and the relationships between them. Mass conversion is something we deal with often, especially when comparing weights in various measurement systems or scaling recipes.

Let's break it down: first, we convert pounds to kilograms, then kilograms to milligrams. Using the conversion factor that 1 pound (lb) is equal to roughly 0.453592 kilograms (kg), you can convert 242 lb to kg like this:
  • Multiply the number of pounds by 0.453592 to get the weight in kilograms.
  • This gives you about 109.772464 kg from 242 lb.
Once converted to kilograms, turning that into milligrams is straightforward. Since 1 kilogram equals 1,000,000 milligrams, just multiply by 1,000,000. You'll have around 109,772,464 mg for 109.772464 kg.

Such conversions are useful in numerous fields like medicine, cooking, and science, where precise measurements are crucial.
Volume Conversion
Volume conversion jumps into the realm of spatial measurements, like changing cubic centimeters to cubic meters. This particular conversion is common in engineering and environmental science, where dimensions often need to be expressed in cubic meters (m³) rather than cubic centimeters (cm³) due to scale differences.

Here's how it works: the conversion factor is that 1 cm³ equals \(1 \times 10^{-6}\) m³. So, for converting 68.3 cm³ to m³, you'll multiply 68.3 by \(1 \times 10^{-6}\). It results in 0.0000683 m³.
  • Remember, to convert from smaller to larger volumes, multiply by a factor of \(10^{-6}\).
  • This conversion helps in understanding the space efficiency of objects, shipping materials, and calculating the capacity of reservoirs.
Having a grip on volume conversions ensures accuracy in measurements needed for large-scale applications, or when precision is key in documenting fluid dynamics and space descriptions.
Metric System
The metric system is an international standard of measurement, widely used across the globe for its simplicity and scalability. It's a decimal-based system, meaning everything is in powers of ten, which makes conversions intuitive.

Units like kilogram, meter, and liter are part of this system. The beauty lies in its structure where each unit's conversion is just a matter of moving the decimal point. For instance, moving from centimeters to meters or grams to kilograms simply involves multiplying or dividing by ten or its powers.
  • The system is standardized and uniform, lessening confusion and errors in scientific data.
  • It is universally adopted, making it easier for scientists and professionals to communicate measurements without converting between various systems.
Adopting the metric system in everyday life and studies ensures you align with global standards, fostering better understanding and collaboration in an increasingly interconnected world.

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Most popular questions from this chapter

Define these terms: (a) matter, (b) mass, (c) weight, (d) substance, (e) mixture.

Three students (X, Y, and Z) are assigned the task of determining the mass of a sample of iron. Each student makes three determinations with a balance. The results in grams are \(X(61.5,61.6,61.4) ; Y(62.8,\) 62.2,62.7)\(; \mathrm{Z}(61.9,62.2,62.1) .\) The actual mass of the iron is \(62.0 \mathrm{~g}\). Which student is the least precise? Which student is the most accurate?

Carry out these operations as if they were calculations of experimental results, and express each answer in the correct units and with the correct number of significant figures: (a) \(7.310 \mathrm{~km} \div 5.70 \mathrm{~km}\) (b) \(\left(3.26 \times 10^{-3} \mathrm{mg}\right)-\left(7.88 \times 10^{-5} \mathrm{mg}\right)\) (c) \(\left(4.02 \times 10^{6} \mathrm{dm}\right)+\left(7.74 \times 10^{7} \mathrm{dm}\right)\) (d) \((7.8 \mathrm{~m}-0.34 \mathrm{~m}) /(1.15 \mathrm{~s}+0.82 \mathrm{~s})\).

A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density \(\left.=0.9986 \mathrm{~g} / \mathrm{cm}^{3}\right) .\) The readings are \(860.2 \mathrm{~g}\) and \(820.2 \mathrm{~g}\), respectively. Given that the density of platinum is \(21.45 \mathrm{~g} / \mathrm{cm}^{3},\) what should her conclusion be based on these measurements? (Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyancy of air.)

Write the equations for converting degrees Celsius to degrees Fahrenheit and degrees Fahrenheit to degrees Celsius.

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