Name: unit conversion steps and real-world errors
Uploaded: 2023-04-30T10:48:05.000Z
Duration: 1 min 36 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.1

PS.1.b

Conversion of Units

단위 변환은 단위를 한 단위에서 다른 단위로 변환하는 프로세스입니다.
SI 단위계는 물리량에 대해 보편적으로 허용되는 표준 단위입니다. 그러나 미국을 포함한 일부 국가에서는 때때로 영국식 단위로 알려진 다른 단위 집합을 사용합니다.
종종 단일 물리량은 다르지만 동등한 단위로 표현될 수 있습니다. 예를 들어, 물체의 길이는 미터 또는 센티미터로 표현할 수 있으며, 여기서 1미터는 100센티미터와 같은 길이를 나타내거나 물체의 질량은 그램 또는 킬로그램으로 표현할 수 있으며, 여기서 1킬로그램은 1000그램과 같습니다.
이러한 등가 단위 간의 변환은 단위 변환 계수를 통해 촉진됩니다.
예를 들어, 미터 또는 센티미터 단위의 길이는 100cm당 1미터 및 1미터당 100cm의 변환 계수를 사용하여 상호 변환할 수 있습니다. 선택의 비율은 결과에서 원하는 단위에 따라 다릅니다.
키가 500센티미터인 기린을 생각해 보십시오. 높이를 미터로 표현하려면 숫자와 단위 모두에 적절한 변환 계수를 곱해야 합니다.
숫자는 제품 수량 5를 산출하고 단위는 미터를 제외한 서로 상쇄됩니다. 따라서 기린의 높이는 5미터와 같습니다.

단위 변환

가끔 한 단위에서 다른 단위로 변환해야 하는 경우가 있습니다. 예를 들어, 양이 리터나 온스 단위로 표시되는 요리책을 읽으려면 양을 컵으로 변환해야 할 수도 있습니다. 또는 어떤 장소까지 가는 방법에 대한 길을 찾을 때 저희는 걸어갈 거리가 몇 킬로미터인지 알고 싶을 수도 있습니다. 이 경우 피트나 미터 단위를 마일로 변환해야 합니다.

단위 변환의 첫 번째 단계는 주어진 단위와 변환에 필요한 단위를 나열하는 것입니다. 두 번째 단계는 주어진 필수 단위와 관련된 변환 계수를 결정하는 것입니다. 변환 계수는 한 단위가 다른 단위와 얼마나 같은지를 나타내는 비율로 정의됩니다. 예를 들어 1km는 1,000m입니다. 변환하는 동안 단위 변환의 단위가 올바르게 변화되서 없어졌는지 확인해야 합니다.

단위 변환의 중요성을 보여주는 잘 알려진 예는 화성 기후 궤도선 발사 사고 였습니다. NASA는 1998년 12월 11일에 이 탐사선을 발사했습니다. 그러나 1999년 9월 23일에 NASA는 화성 주변의 계획된 궤도로 탐사선을 유도하려고 시도하는 동안 탐사선과의 접촉이 끊어졌습니다. 후속 조사에 따르면 스러스터를 기록하고 구동하는 데 사용된 두 프로그램의 장치가 동기화되지 않은 것으로 나타났습니다. 이 오류로 인해 탐사선은 NASA가 예상한 것과 매우 다른 궤적을 따르게 되었고, 이로 인해 탐사선은 화성 대기에서 불타버리거나 우주로 발사되었습니다. 단위 변환에 주의를 기울이지 않아 과학자와 엔지니어가 프로젝트에 소비한 시간은 말할 것도 없고 이로 인해서 수억 달러의 비용이 발생했습니다.

이 텍스트는 <a href="https://openstax.org/books/university-physics-volume-1/pages/1-3-unit-conversion">Openstax, University Physics Volume에서 발췌되었습니다. 1, 섹션 1.3: 단위 변환</a>.

때로는 한 장치에서 다른 단위로 변환해야 할 필요가 있습니다. 예를 들어, 수량이 리터 단위로 표시되는 요리책을 읽는 것은 ...

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

Units, Dimensions, and Measurements

단위, 차원 및 측정

KEY TERMS AND CONCEPTS

주요 용어 및 개념

unit conversion steps and real-world errors

Unit conversion lets you change a measurement from one unit to another. It is useful in everyday life, such as when a cookbook gives amounts in liters or ounces and you need cups instead. It also helps when directions use feet or meters, but you want to know the distance in miles.

The first step is to list the given unit and the unit you need. The second step is to choose a conversion factor, which is a ratio that shows how many of one unit equal another unit. For example, 1,000 meters equal 1 kilometer.

During the conversion, the units must cancel correctly. This keeps the calculation organized and gives the right final unit. Unit conversion is important in science and engineering because small unit mistakes can lead to major problems.

A well-known example is the Mars Climate Orbiter. NASA launched the probe on December 11, 1998, and lost contact with it on September 23, 1999 while trying to place it in orbit around Mars. Investigators found that the two programs used different units for recording and driving the thruster. That mismatch sent the probe on the wrong path, where it burned up in the Martian atmosphere or flew out into space. The error cost hundreds of millions of dollars and much time for the scientists and engineers involved.

Unit Conversion Steps and Real-World Errors

unit-conversion-steps-and-real-world-errors

the scope of physics

How Physics Shapes Science and Technology

Physics studies the interactions of energy, matter, space, and time. It looks for the basic mechanisms that explain natural phenomena. The word physics comes from the Greek word physis, which means nature. Physics helps us understand the natural world at its most fundamental level. It relies on quantitative laws, or rules written in numbers and measurements, to describe how things behave. That approach can also help other fields improve the limits of current technology. Physics matters in...

orders of magnitude

Estimating Scale with Powers of 10

Orders of magnitude help estimate the scale of a number using powers of 10. It is a simple way to round values to the nearest power of 10. This makes it easier to compare very large and very small numbers. To find the order of magnitude of a number, take its base-10 logarithm and round to the nearest integer. The result gives the power of 10 that most closely matches the original value. This method gives a consistent estimate of size without using exact digits. Orders of magnitude are useful...

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models, theories, and laws

Scientific Models, Theories, and Laws

Scientific models, theories, and laws help physicists describe natural phenomena. A model is a simplified version of a physical system that is too complex to study in full. It acts as a rough mental or visual picture of what may be happening. Good models keep the important parts and simplify the rest so the problem becomes workable. The light wave model is one example. Light waves are usually invisible, so they cannot be seen in the same way as water waves. Even so, it is useful to think of...

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units and standards of measurement

SI Units for Physical Quantities

SI units give a standard way to measure physical quantities. A physical quantity can be defined by how it is measured or by how it is calculated from other measurements. For example, the mass and dimensions of a metallic cube can be found with a weighing machine and a meter scale. Some quantities are built from others. The volume of a cube is the cube of its side length. The density of the cube is then found by dividing mass by volume. Measurements are written in units, which are standardized...

estimation of the physical quantities

Fermi Estimation for Physical Quantities

Fermi estimation helps physicists, scientists, and engineers make rough calculations for physical quantities. These estimates are also called guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. Enrico Fermi was known for making these kinds of estimates with surprising precision. Estimation is not random guessing. It uses prior experience and sound physical reasoning to get a rough value for a quantity. This kind of reasoning helps build...

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base quantities and derived quantities

SI Base Units Behind Measured Quantities

SI base units are the starting point for measuring physical quantities. In any system of units, some quantities must be defined through direct measurement. These are called base quantities, and their units are base units. Other physical quantities are built from these base values by algebraic combinations. These are called derived quantities, and their units are derived units. For example, area comes from two lengths multiplied together. It is a derived quantity and is written in SI base units...

conversion of units

Unit conversion lets you change a measurement from one unit to another. It is useful in everyday life, such as when a cookbook gives amounts in liters or ounces and you need cups instead. It also helps when directions use feet or meters, but you want to know the distance in miles. The first step is to list the given unit and the unit you need. The second step is to choose a conversion factor, which is a ratio that shows how many of one unit equal another unit. For example, 1,000 meters equal 1...

accuracy and precision

Repeated Measurements in Science

Repeated measurements help scientists check the quality of their results. They are used to judge both precision and accuracy. These two ideas are related, but they do not mean the same thing. Measurements are precise when repeated trials give very similar results. Precision shows how closely the values agree with one another. Measurements are accurate when the result is very close to the true value or the accepted value. Accuracy shows how closely the values agree with the real target. High...

random and systematic errors

How Measurement Errors Affect Results

Measurement errors can change how accurate and precise a result appears. Scientists try to record measurements as carefully as possible, but errors can still happen. These errors are usually random or systematic. Random errors come from inconsistency or fluctuation in the measuring process. They can also come from changes in the quantity being measured. In repeated measurements, random error may make a value appear greater than the true value one time and less than it the next. A simple...

rules for significant figures

Measurement Precision and Significant Figures

Measurement precision depends on the tool used, and significant figures show that precision. A ruler can measure length to the closest millimeter. A caliper can measure length to the nearest 0.01 mm, so it gives a more precise measurement because it can detect very small changes in length. When a value is written from a measurement, the last digit is not exact. The person making the measurement must estimate that digit. For example, a stick that seems to fall between 13.2 cm and 13.3 cm must...

significant figures in calculations

Rounding Rules for Significant Figures

Rounding rules for significant figures help show the right level of certainty in measured results. When a calculation is reported with the correct number of significant figures, it better matches the uncertainty in the measurements. The rounding rule depends on the type of math being done. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. For multiplication and division, the result should have the same number of...

dimensional analysis

Dimensional Checks in Physics Equations

Dimensional consistency is a key check in physics equations. It means the dimensions on both sides of an equation must match. The idea helps show whether an equation can represent a real physical law. The first rule is simple: expressions on each side of the equal sign must have the same dimensions. That makes sense because you can only add or subtract quantities of the same type. The second rule says that the input to a standard mathematical function, such as a trigonometric function, a...

problem solving: dimensional analysis

Dimensional Checks for Physics Equations

Dimensional analysis helps check whether physics equations make sense. It compares the dimensions on each side of an equation and shows whether the units are consistent. This method is useful for spotting algebra errors, typos, and for remembering physical laws. A valid equation must follow two rules. First, both sides of an equality must have the same dimension, so only quantities with matching dimensions can be added or subtracted. Second, common math functions such as exponential,...

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solving problems in physics

Physics Problem Solving: Strategy to Check

Physics problem solving uses general physical principles to work out specific situations. It is a key skill in physics, and it can also help with everyday life. The same analytical skills can be used in new situations, while a list of facts can never cover every possible case. Solving physics problems also takes creativity and insight. These skills grow with experience and practice. There is no simple step-by-step method that works for every problem, but a three-stage process can guide the...

key terms and concepts

Learn how to convert units using conversion factors, unit cancellation, and clear steps. See how a unit mismatch helped cause the Mars Climate Orbiter failure.

Unit Conversion Steps and Real-World Errors | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

PH.1

PH.1.b

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.1

CHEM.1.E

Scientific Method

The scientific method is used to solve problems and explain phenomena. The development of the scientific method coincided with changes in philosophy ...

What is a Hypothesis?

A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about ...

Null and Alternative Hypotheses

The actual hypothesis testing begins by considering two hypotheses. They are termed&#160; the null hypothesis and the alternative hypothesis. These ...

Types of Hypothesis Testing

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed ...

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their ...

Hypothesis Test for Test of Independence

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test ...

Decision Making: P-value Method

The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a ...

Decision Making: Traditional Method

The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using ...

empirical-method-to-interpret-standard-deviation

Empirical Method to Interpret Standard Deviation

The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The ...

Data Collection by Experiments

Data collection is a systematic method of obtaining, observing, measuring, and analyzing accurate information. An experimental study is a standard method ...

Solving Problems in Physics

Problem-solving is the ability to apply general physical principles to specific situations, usually expressed by equations. It is an essential skill in ...

The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
• ask questions that require empirical evidence to answer
• develop hypotheses indicating relationships between independent and dependent variables
• offer simple solutions to design problems

PS.1.a

What is an Experiment?

An experiment is a planned activity carried out under controlled conditions. The purpose of an experiment is to investigate the relationship between two ...

Study Design in Statistics

A study design is a set of techniques that allow a researcher to collect and analyze data from different variables defined for a specific research ...

Observational Studies

Observational studies are a type of analytical study where researchers observe events without any interventions. In other words, the researcher does not ...

Experimental Designs

An experimental design is a systematic process that allows researchers to evaluate the relationship between dependent and independent variables. There are ...

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally ...

Crossover Experiments

Crossover experiments, also called the repeated-measurements design, is a study design in which all experimental units are exposed to all treatments in ...

Controls in Experiments

When conducting an experiment, it is crucial to have control to reduce bias and accurately measure the dependent variables. It also marks the results more ...

Bias

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected ...

Blinding

Blinding is a commonly used method of not telling participants which treatment a subject is receiving. Blinding is a critical part of a randomized control ...

Clinical Trials

Clinical trials are prospective experimental studies conducted on humans to determine the safety and efficacy of treatments, drugs, diet methods, and ...

Data Collection by Observations

Data collection refers to a systematic way of obtaining, observing, measuring, and analyzing accurate information. Observational studies are one of the ...

Data Collection by Survey

The systematic method of obtaining and analyzing accurate information of a population is called data collection. A survey is a standard method of data ...

Units and Standards of Measurement

A physical quantity is defined either by specifying its measurement method or by stating how it is calculated from other measurements. For example, ...

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as ...

Base Quantities and Derived Quantities

In any system of units, the units for some physical quantities must be specified through a measurement process. These measurements are the base quantities ...

Sometimes, there is a need to convert from one unit to another one. For instance, reading a cookbook in which quantities are expressed in units of liters ...

The student will demonstrate an understanding of scientific and engineering practices by planning and carrying out investigations
• independently and collaboratively plan and conduct observational and experimental investigations; identify variables, constants, and controls where appropriate and include the safe use of chemicals and equipment
• evaluate the accuracy of various methods for collecting data
• take metric measurements using appropriate tools and technologies
• apply scientific ideas or principles to design, construct, and/or test a design of an object, tool, process or system

Review and Preview

Data are individual items of information obtained from a population or sample. Data may be classified as qualitative (categorical), quantitative ...

What is a Frequency Distribution

A frequency is the number of times a value of the data occurs. The sum of all the frequency values represents the total number of students included in the ...

Ogive Graph

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, ...

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data ...

Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. ...

Scatter Plot

The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a ...

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct ...

Bar Graph

A bar graph is also called a bar chart and consists of bars that are separated from each other. It either uses horizontal or vertical bars to show ...

Multiple Bar Graph

As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can ...

Pareto Chart

A Pareto chart is a bar graph or a combination of both line and bar graphs. The bar lengths represent the individual values or the frequency, while the ...

Pie Chart

A pie chart (or a pie graph) is a circular graphical chart or a pictorial representation of categorical data. It is divided into slices of pie each ...

What is Central Tendency?

Descriptive statistics describe or summarize relevant characteristics of a sample and aid in the analysis of data of interest. When analyzing large ...

What is Variation?

Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of ...

Range

The range is one of the measures of variation. It can be defined as the difference between a dataset&#39;s highest and lowest values. For example, in the ...

Standard Deviation

The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The ...

Calculating Standard Deviation

The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. ...

Variance

&#160;The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative ...

Coefficient of Variation

The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can ...

Contingency Table

A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution ...

Statistical Analysis: Overview

An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...

The student will demonstrate an understanding of scientific and engineering practices by pnterpreting, analyzing, and evaluating data
• construct and interpret data tables showing independent and dependent variables, repeated trials, and means
• construct, analyze, and interpret graphical displays of data and consider limitations of data analysis
• apply mathematical concepts and processes to scientific questions
• use data to evaluate and refine design solutions to best meet criteria

PS.1.c

Models, Theories, and Laws

Scientists frequently use models to help them comprehend a specific collection of phenomena. In physics, a model is a condensed version of a physical ...

Inductive Reasoning

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in ...

Deductive Reasoning

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the ...

The student will demonstrate an understanding of scientific and engineering practices by constructing and critiquing conclusions and explanations
• construct scientific explanations based on valid and reliable evidence obtained from sources (including the students' own investigations)
• construct arguments supported by empirical evidence and scientific reasoning
• generate and compare multiple solutions to problems based on how well they meet the criteria and constraints
• differentiate between a scientific hypothesis, theory, and law

PS.1.d

The student will demonstrate an understanding of scientific and engineering practices by developing and using models
• construct, develop, and use models and simulations to illustrate and/or explain observable and unobservable phenomena
• evaluate limitations of models

PS.1.e

The Scientific Method

Chemistry is an empirical science. Scientists often pose questions to understand the chemistry in everyday life and seek answers to these questions. To ...

The student will demonstrate an understanding of scientific and engineering practices by obtaining, evaluating, and communicating information
• read scientific texts, including those adapted for classroom use, to determine the central idea and/or obtain scientific and/or technical information
• gather, read, and synthesize information from multiple appropriate sources and assess the credibility, accuracy, and possible bias of each publication
• construct, use, and/or present an oral and written argument supported by empirical evidence and scientific reasoning

PS.1.f

Unit Conversion Steps and Real-World Errors

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