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Chapter 1: Problem 54

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) \mum to mm, (b) ms to ns, (c) mi to km, (d) \(\mathrm{ft}^{3}\) to \(\mathrm{L}\) .

Short Answer

Expert verified
To convert the given units, we can use the following conversion factors: (a) 1 mm = 1,000 碌m, so 1 碌m * (1 mm / 1,000 碌m). (b) 1 ms = 1,000,000 ns, so 1 ms * (1,000,000 ns / 1 ms). (c) 1 mi = 1.60934 km, so 1 mi * (1.60934 km / 1 mi). (d) 1 ft^3 = 28.3168 L, so 1 ft^3 * (28.3168 L / 1 ft^3).

Step by step solution

01

(a) Converting micrometers to millimeters

To convert 碌m to mm, we need the conversion factor for micrometers and millimeters. We know that: 1 millimeter (mm) = 1,000 micrometers (碌m) Now, we can set up the conversion using the given conversion factor: 1 碌m * (1 mm / 1,000 碌m) The 碌m unit cancels out, leaving us the converted value in mm.
02

(b) Converting milliseconds to nanoseconds

To convert ms to ns, we'll need the conversion factor for milliseconds and nanoseconds. We know that: 1 millisecond (ms) = 1,000,000 nanoseconds (ns) Now, we can set up the conversion using the given conversion factor: 1 ms * (1,000,000 ns / 1 ms) The ms unit cancels out, leaving us the converted value in ns.
03

(c) Converting miles to kilometers

To convert mi to km, we'll need the conversion factor for miles and kilometers. We know that: 1 mile (mi) = 1.60934 kilometers (km) Now, we can set up the conversion using the given conversion factor: 1 mi * (1.60934 km / 1 mi) The mi unit cancels out, leaving us the converted value in km.
04

(d) Converting cubic feet to liters

To convert ft^3 to L, we'll need the conversion factor for cubic feet and liters. We know that: 1 cubic foot (ft^3) = 28.3168 liters (L) Now, we can set up the conversion using the given conversion factor: 1 ft^3 * (28.3168 L / 1 ft^3) The ft^3 unit cancels out, leaving us the converted value in L.

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Key Concepts

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

Metric System
The Metric System is a uniform way of measuring that is used worldwide due to its simplicity and ease of conversion between different units. It is a decimal-based system, meaning it works in powers of ten. This makes calculations and conversions straightforward. For example, converting micrometers to millimeters is simple because both units are part of the same system. To convert between metric units, there's usually a base conversion factor based on powers of ten:
  • 1 kilometer (km) = 1,000 meters (m)
  • 1 meter (m) = 1,000 millimeters (mm)
  • 1 millimeter (mm) = 1,000 micrometers (碌m)
Makes it easy, right? You just move the decimal point to convert between units. When you understand how the metric system is structured, it becomes very intuitive to move from one unit to the next.
SI Units
The SI Units, often called the International System of Units, are an extension of the metric system. This system is universally accepted for scientific and technical use. It comprises base units and derived units that provide a cohesive framework for measurement. The advantage of SI units is their standardization, facilitating global communication in science and industry. Some base units include:
  • The meter (m) for distance
  • The kilogram (kg) for mass
  • The second (s) for time
Derived units, like the liter (L) for volume or the millisecond (ms) for time intervals, are based on these fundamental units, adhering to the consistent logic of the SI system. Using SI units ensures that measurements are precise and reliable, no matter where they are taken or reported.
Conversion Factors
A Conversion Factor is a number used to change one set of units to another, by multiplying or dividing. It allows us to switch between unit systems seamlessly. Each conversion factor is derived from the ratio of two equivalent measurements in different units. For example, converting units requires also setting up a proper equation where units cancel out:
  • To convert micrometers (碌m) to millimeters (mm), use the factor 1 mm = 1,000 碌m.
  • For milliseconds (ms) to nanoseconds (ns), the factor is 1 ms = 1,000,000 ns.
  • Converting miles to kilometers involves a factor of 1 mi = 1.60934 km.
  • From cubic feet (ft鲁) to liters (L), use 1 ft鲁 = 28.3168 L.
By applying these conversion factors, you transform quantities from one unit to another accurately. They are essential tools in practical calculations, bridging different unit measurements effectively.

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Most popular questions from this chapter

Consider the two spheres shown here, one made of silver and the other of aluminum.(a) What is the mass of each sphere in \(\mathrm{kg}\) ( b) The force of gravity acting on an object is \(F=m g\) where \(m\) is the mass of an object and \(g\) is the acceleration of gravity \(\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right) .\) How much work do you do on each sphere it you raise it from the floor to a height of 2.2 \(\mathrm{m} ?(\mathrm{c})\) Does the act of lifting the sphere off the ground increase the potential energy of the aluminum sphere by a larger, smaller, or same amount as the silver sphere? (d) If you release the spheres simultaneously, they will have the same velocity when they hit the ground. Will they have the same kinetic energy? If not, which sphere will have more kinetic energy? \([\) Section 1.4\(]\)

Judge the following statements as true or false. If you believe a statement to be false, provide a corrected version.(a) Air and water are both elements. (b) All mixtures contain at least one element and one compound.(c) Compounds can be decomposed into two or more other substances; elements cannot. (d) Elements can exist in any of the three states of matter. (e) When yellow stains in a kitchen sink are treated with bleach water, the disappearance of the stains is due to a physical change. (f) A hypothesis is more weakly supported by experimental evidence than a theory. (g) The number 0.0033 has more significant figures than 0.033 . (h) Conversion factors used in converting units always have a numerical value of one. (i) Compounds always contain at least two different elements.

A watt is a measure of power (the rate of energy change) equal to 1 \(\mathrm{Js.}(\mathbf{a})\) Calculate the number of joules in a kilowatt-hour. (b) An adult person radiates heat to the surroundings at about the same rate as a 100 -watt electric incandescent light bulb. What is the total amount of energy in kcal radiated to the surroundings by an adult over a 24 h period?

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52\(\%\) . The students' results for three determinations are as follows: $$\begin{array}{l}{\text { (1) } 22.52,22.48,22.54} \\ {\text { (2) } 22.64,22.58,22.62}\end{array}$$ (a) Calculate the average percentage for each set of data and state which set is the more accurate based on the average. (b) Precision can be judged by examining the average of the deviations from the average value for that data set. (Calculate the average value for each data set; then calculate the average value of the absolute deviations of each measurement from the average.) Which set is more precise?

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the con- version factors needed to convert (a) mm to nm, (b) mg to kg, (c) km to ft, (d) in. \(^{3}\) to \(\mathrm{cm}^{3} .\)
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