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The micrometer \((1 \mu \mathrm{m})\) is often called the micron. (a) How many microns make up \(1.0 \mathrm{~km} ?\) (b) What fraction of a centimeter equals \(1.0 \mu \mathrm{m} ?\) (c) How many microns are in 1.0 yd?

Short Answer

Expert verified
(a) 1.0 km = 1.0 billion microns; (b) 1.0 μm = 1/10,000 of a cm; (c) 1.0 yd = 914,400 microns.

Step by step solution

01

Convert Kilometers to Microns

First, understand the relationship between kilometers, meters, and microns. We know that: 1 kilometer = 1000 meters, and 1 meter = 1,000,000 microns. Multiply the number of meters in a kilometer by the number of microns in a meter:\[1.0\text{ km} = 1.0 \times 1000\text{ m} \times 1,000,000\text{ microns/m} = 1.0 \times 10^9 \text{ microns}\]
02

Convert Micron to Fraction of a Centimeter

Next, we need to find what fraction of a centimeter a micron represents. 1 centimeter = 10 millimeters = 10,000 microns. Thus, 1 micron is 1/10,000 of a centimeter:\[1.0 \mu\mathrm{m} = \frac{1}{10,000} \text{ of a centimeter}\]
03

Convert Yards to Microns

Lastly, convert yards to microns. We know:1 yard = 0.9144 meters, and 1 meter = 1,000,000 microns. Therefore, multiply the number of meters in a yard by the number of microns in a meter:\[1.0\text{ yd} = 0.9144\text{ m} \times 1,000,000\text{ microns/m} = 914,400\text{ microns}\]

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Key Concepts

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

Understanding Unit Conversion
Unit conversion is an essential skill in science and everyday life. It involves changing a measurement from one unit to another, which can be of the same system or even different systems. This process requires knowing the conversion factors between different units.

For instance, converting kilometers to microns involves using the fact that 1 kilometer equals 1000 meters, and 1 meter equals 1,000,000 microns. By multiplying these factors, we can easily convert between these units. Similarly, when converting yards to microns, we first find that 1 yard equals 0.9144 meters and then apply the same meter-to-micron conversion. Understanding these relationships helps in precise scientific calculations. It also ensures we retain accuracy when measuring different dimensions.
Exploring the Micrometer
The micrometer, often called a micron, is a unit of length in the metric system that equals one-millionth of a meter (1 micron = 1 µm = 0.000001 meters).

This small measurement is used to express dimensions at a microscopic level, such as the thickness of human hair or the size of bacteria and other microorganisms. Because it represents such a tiny length, micrometers are extremely helpful in scientific studies that require precision at micro scales.

In addition, when converting microns to other units, such as seeing what fraction of a centimeter a micron represents, it helps to realize that a centimeter contains 10,000 microns, resulting in a conversion factor of 1 micron being 1/10,000 of a centimeter. This demonstrates the micrometer's significant role in measurement scales.
The Metric System: A Universal Language
The metric system is a standardized system of measurement used by most of the world. It is based on powers of ten, making it straightforward to convert between different units of measurement.

Key units include meters for length, grams for weight, and liters for volume, along with their multiples and submultiples like kilometers or micrometers. Because of this simplicity, the metric system is highly efficient, with consistency reducing the chances for errors in calculations.

Being familiar with the metric system allows us to easily understand and convert measurements, such as moving between meters, kilometers, and microns. It powers scientific research, engineering, and international commerce, demonstrating its fundamental role in our modern world.
Principles of Measurement
Measurement is the process of determining the size, length, or amount of something, usually expressed in standard units. It serves as the foundation of science and engineering, providing a way to quantify and understand the physical world.

Accurate measurements are crucial since they ensure reliable data. This involves using the right instruments and ensuring units are correctly reported and understood. When you convert units, like meters to microns or meters to yards, it means adjusting the scales without altering the actual quantity.

Having a broad understanding of measurement concepts enables us to grasp and work with various levels of precision, such as those required in fields like physics or biology. This understanding facilitates meaningful comparison, communication, and interpretation of data across different regions and disciplines.

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Most popular questions from this chapter

As a contrast between the old and the modern and between the large and the small, consider the following: In old rural England 1 hide (between 100 and 120 acres) was the area of land needed to sustain one family with a single plough for one year. (An area of 1 acre is equal to \(4047 \mathrm{~m}^{2} .\) ) Also, 1 wapentake was the area of land needed by 100 such families. In quantum physics, the cross-sectional area of a nucleus (defined in terms of the chance of a particle hitting and being absorbed by it ) is measured in units of barns, where 1 barn is \(1 \times 10^{-28} \mathrm{~m}^{2}\). (In nuclear physics jargon, if a nucleus is "large," then shooting a particle at it is like shooting a bullet at a barn door, which can hardly be missed.) What is the ratio of 25 wapentakes to 11 barns?

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel consumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs from the U.S. gallon: $$ \begin{aligned} 1 \mathrm{U} . \mathrm{K} . \text { gallon } &=4.5460900 \text { liters } \\ 1 \mathrm{U.S} . \text { gallon } &=3.7854118 \text { liters. } \end{aligned} $$ For a trip of 750 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

A vertical container with base area measuring \(14.0 \mathrm{~cm}\) by \(17.0 \mathrm{~cm}\) is being filled with identical pieces of candy, each with a volume of \(50.0 \mathrm{~mm}^{3}\) and a mass of \(0.0200 \mathrm{~g}\). Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of \(0.250 \mathrm{~cm} / \mathrm{s}\) at what rate (kilograms per minute) does the mass of the candies in the container increase?

Water is poured into a container that has a small leak. The mass \(m\) of the water is given as a function of time \(t\) by \(m=5.00 t^{0.8}-3.00 t+20.00,\) with \(t \geq 0, m\) in grams, and \(t\) in seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? In kilograms per minute, what is the rate of mass change at \((\mathrm{c}) t=2.00 \mathrm{~s}\) and (d) \(t=5.00 \mathrm{~s} ?\)

In purchasing food for a political rally, you erroneously order shucked medium-size Pacific oysters (which come 8 to 12 per U.S. pint) instead of shucked medium-size Atlantic oysters (which come 26 to 38 per U.S. pint \() .\) The filled oyster container shipped to you has the interior measure of \(1.0 \mathrm{~m} \times 12 \mathrm{~cm} \times 20 \mathrm{~cm},\) and a U.S. pint is equivalent to 0.4732 liter. By how many oysters is the order short of your anticipated count?

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