Introduction to Units - Online Tutor, Practice Problems & Exam Prep

Physics involves the study of natural phenomena through measurements and equations, primarily using the SI system of units like kilograms (kg), meters (m), and seconds (s). Understanding unit compatibility is crucial for accurate calculations, as seen in the equation for force: $F^2=ma$. Metric prefixes simplify large or small numbers, while scientific notation compresses lengthy values, enhancing clarity in communication and calculations.

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Hello everyone, and welcome to Pearson Plus for physics. My name is Patrick, and I'll be your main guide throughout our content. It's my job to help you actually understand the concepts you see from lecture to help you prepare for your exams. I have a bachelor's degree in physics and I've been helping college-level physics students since 2012. I love to make science interesting, but more importantly, I love giving students the skills and tools that they need to be successful in their courses.

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Introduction to Units & the SI System

Hey, guys. Welcome to Physics. My name is Patrick. I want to be your instructor. For this first video, we're just going to talk about briefly units and the SI system of units. Let's check it out. So guys, what's physics all really about? Well, physics is the study of natural phenomena. That's the definition you'll see in your textbook. But really, it's just a bunch of measurements and a lot of equations. I like to think about physics as a math class with rules or math with a storyline. For example, if you take a ball and you drop it towards the ground, it falls to the ground because of gravity. That's a rule. There's also a math equation to describe how fast and how far it falls. And so before we get to the equations, which we'll see plenty of in the future, I want to talk about measurements and units because in nature we measure physical quantities. So things like mass, length, and time, all the stuff that I have in this table down here that we'll get to in just a second. And the thing about these measurements or physical quantities is that when you measure something, you have to have a number and a unit in order for it to make sense. For example, let's say you measure the mass of a box. Need a number and a unit to describe it. If you just said that mass was 10, 10 by itself doesn't actually mean anything. It could be 10 kilograms or ten pounds. So if you have just 10, that doesn't mean anything. But if you measure it to be 10 kilograms, now that's a number and a unit and that measurement does make sense. Now, kilograms, a lot of these units will have their shorthand notations. We're going to see a bunch of those things later on in the future. So, we're going to see a lot of units in physics. And so, in order for your equations to work, what you have to remember is that all the units inside of that equation must be compatible with each other. So the way I like to think about that is they kind of have to speak the same language. And so groups of compatible units that speak the same language or work together form what's called a system of equations. And in physics, the big one is going to be the SI system, which stands for, in French, the System International. So it's just backwards. So this is the SI system. We've already been exposed to kilograms which is kg and meters is m, seconds is s, and newtons is n. There are other systems that we'll see. The imperial system is an example where we're using pounds, feet, inches, seconds, things like that. But the main one that we use in physics is the SI system. So physics equations, in order for them to work, all the units must be compatible with each other. Here's a quick example. One of the most powerful equations you'll see in physics is going to be force equals mass times acceleration or F=ma. So if we replace all these variables with their units, we can see that a Newton is equal to a kilogram times acceleration. And I'm just going to give this to you. Acceleration is in units of meters per second squared. So notice how all of these units here, newtons, kilograms, meters, and seconds, all belong to the SI unit system. Whereas if I said a Newton equals a pound times a meter per second squared, this is actually incompatible whereas this first equation is compatible. So this is actually incorrect and you're going to get a wrong answer if you start mixing and matching things from different systems. So make sure that all your equations and all the units speak the same language and are compatible. Alright, guys. That's really all there is to it for this one. Let's move on to the next video.

Metric Prefixes

Hey, guys. So now that we've seen SI units in the SI unit system, a lot of times you're gonna see letters or symbols that get attached to your base units. Your base units are just meters, grams, and seconds. They're kind of like the most simplistic basic units of, or metric units. So we're gonna see letters like k or m or even Greek letters like mu. These are called metric or SI unit prefixes. And the basic idea is that each one of these letters is just a shorthand for a prefix like k for kilo, m for milli, or mu for micro. And each one of these prefixes or letters just stands for a specific power of 10 that you're gonna multiply by a base unit. So for instance, kilo is 103. Micro is 10-6. They're kind of just like easy ways to represent big and small numbers, so you don't have to write a bunch of zeros out. For example, 5 kilometers or 5 kilometers is gonna be, if we wanted to represent that in terms of meters, we would just look up k inside of our table. We know k stands for kilo and the prefix kilo stands for 103 or 1,000, means the same thing. So 5 kilometers just means 5 times 1,000 meters. So 5 kilometers is just the same thing as 5,000 meters.

Here's another example. 4.6 ms. So here we're gonna look up this prefix m, which by the way is not the same thing as our base unit of meters. Same letter but different meaning. So we're gonna look up this m and m stands for milli. And this milli prefix stands for a specific power of 10, 10-3 or 1,000. They're 0.001. All those things mean the same thing. So 4.6 milliseconds just means 4.6 times 0.001 seconds. So these prefixes just help us write these numbers in just a more compact way. So we're gonna use this table a lot actually because you're gonna have to convert between the metric prefixes. So I'm gonna give you a really simple process for doing this. Let's just do a bunch of examples and see how this works.

So we're gonna express the following measurements and we're gonna basically rewrite them in the desired prefix. So let's just get to the first one. We're gonna convert 6.5 to m. Here's the first thing you're always gonna do when you're rewriting these using metric prefixes. You're gonna identify where your starting and target prefixes are. So here, I'm starting at h. So h stands for hecto. And then I'm actually going to no base unit. So I'm actually going to no prefix. So that's actually I'm sorry. No prefix. So that's the base unit. So I'm really just going from here to here. So what I have to do is the next step is I have to move from the start to the target, and I'm just gonna count up the number of exponents that I moved. For example, I'm going from hecto to base unit. So I'm going from 102 to 100. So if I move from here to here, then I've jumped 2 exponents. So I've really gone 2 to the right here. And it's important that you figure out the direction because that leads us to the third step, which is we're gonna shift the decimal place in the same direction that we moved in step 2. So for example now, 6.5 hm, we shifted 2 to the right. So in terms of meters now, you just take the decimal place and you shift it to the right twice, and you fill in a 0 as needed. So 6.5 hectometers is the same thing as 650 meters. That's really all there is to it. Just follow these steps and we'll always get the right answer.

Let's just do a few more so we get comfortable with this. So, 3.89 millimeters to meters. So here we have this prefix, M. So this is milli, and we're gonna go to the base unit, which is in meters. So we're gonna do the exact same procedure. Here I'm starting off at milli and I wanna go towards the base unit. So I'm just gonna go from start to finish, or from start to target, and I'll count up the number of exponents that I moved. So I'm going from 10-3 to 0. Just look at the number. Don't worry about the sign. We actually jumped 3 to the left. So from here to here, we jumped 3 to the left. So that means that 3.89 millimeters if I wanna write this in terms of meters, I'm gonna write the number 3.89, but I have to shift it to the left three times. Right. So I have to shift it to the left because that's the same direction I moved in step 2. So 1, 2, 3. And so, I'm gonna fill in zeros along the way, and then I'm gonna put another 0 point, so that the decimal point is, like, right here. So that's 0.00389 meters, and that's our answer.

Now for this last one here, we're gonna convert or we're going to rewrite, 7.62 kilograms to micrograms. So here, we just identify the prefixes. I'm going from kilo, and then eventually, I'm gonna end up at micro. So here's what I'm gonna do. I'm gonna shift from start to the target. So from 103, I'm gonna have to cross through the 0 exponents. So when I move in this direction, I'm actually going 3 exponents. And then from 0 over to micro, which is 10-6, then I'm jumping actually 6 exponents. So in total, I've actually moved 9 to the right. And so, therefore, I'm just gonna shift the exponent to the right 9 times. So 7.62 kilograms becomes I'm just gonna shift it 1, 2, and then 1, 2, 3, 4, 5, 6, 7. So it's 1,2,3,4,5,6,7,8,9, and I'm gonna fill in 7 zeros along the way. And so that is how you would convert how you would rewrite 7.62 kilograms to micrograms. So we can see here like kind of a pattern. And so when you're rewriting these numbers with, with metric prefixes, there's a pretty easy rule to follow to check, you know, if you're if you're doing the right thing. If you're shifting from a bigger to a smaller unit, basically going to the right, then your number is going to become larger. So if your units are becoming smaller, there should be more of them. That's the way to think about that. And if you're going from a smaller to a bigger unit, then your number is going to become smaller. Alright, guys. That's it for this one. Let me know if you have any questions.

The earth's circumference is approximately 40.1 Mm (megameters). What is this circumference in kilometers?

• A. 0.0401 km
• B. 40,100,000 km
• C. 40,100 km
• D. 0.00401 km

Astronomers often detect radio waves with wavelengths of 3,000,000,000 nm. What is this wavelength expressed in decameters (dam)?

• A. 3 dam
• B. 0.3 dam
• C. 30 dam
• D. 0.03 dam

Scientific Notation

Guys, so a lot of times in physics, we're going to work with really long numbers whether they're really big or really small. For example, the mass of the Earth is a crazy long number here. Imagine we had to write this out every single time we used it. Well, fortunately, we can use a type of notation called scientific notation, and we use scientific notation to compress really long inconvenient numbers into much shorter ones. For example, we can take this long number here with a bunch of zeros, and we can rewrite the mass of the Earth as 5.97×1024 kilograms. So this is a much shorter way of representing that number. So, the general format for scientific notation is going to be a number a.bc×10d. a.bc is just going to be a number that's greater than or equal to 1, but less than 10, for example, 5.97. Then, that's the number, and you're going to multiply it by 10d. This d is just an exponent. So, how do we actually get all these numbers? I'm going to show you a really simple process for how we convert or how we rewrite standard form into scientific notation. Standard form is just normal numbers and then into scientific notation. Let's just do a bunch of examples so we get the hang of this. So, we're going to take this number and rewrite it in scientific notation. The first thing you're going to do is you're going to move the decimal place until you get to a number that's between or greater than or equal to 1, but less than 10. So here, the decimal place is over here, and we have to move it to the left. 1, 2, 3, 4, and then 5. So we're going to move it 5 decimal places to the left in order to land at this number 3.04. The next thing we want to do is round this number to the second decimal place if it's a really long number with a lot of non-zero numbers, like this one is. So we're going to take this and we're going to round it to the second decimal place. So we're going to have to look at the next digit over here, and it's greater than 5, so we're going to have to round it up. So, I'm going to round this up to 3.05, and I'm going to multiply it by 10, and now I have to figure out what the exponent is. Well, that's the 3rd step. The 3rd step is the number of decimal places that you moved in the first step is going to be equal to your exponent. And if you came from an original number that's greater than 10, that exponent is positive. So, for example, we moved from a number the original number greater than 10, we move 5 spaces to the left, so our exponent is positive 5. And that's how you rewrite this number. That's really all there is to it. Let's do a couple more examples so we get the hang of this. So now we're going to do the same thing over here. We now have to move the decimal place until we get a number that's between 1 and 10. So we actually have to shift it forward 2, 3, 4. So there were actually 4 spaces to the right that we moved here. So we end up with is a number that's 1.02, we don't have to round it or anything, times 10. And now, we have to figure out the exponent. Well, we came from an original number that was less than 1, so our exponent is negative. So it's 10-4. The 4 means the number of decimal places that we moved. And now you might also see some weird ones. You might also see, like, you might have to you know, your professor might ask you to represent 7 in terms of scientific notation. So we're going to follow the same exact steps. Move the decimal place until we get to a number that's between 1 and 10. But if you think about it, the decimal place is right here, and this odd number is already between 1 and 10. So the way you would write this is 7, you don't have to move it, times 10, and the number of decimal places is equal to your exponent. But you didn't actually move any decimal places, so this is just times 100. Just in case you see some weird stuff like this, this is actually how you would represent this in scientific notation. Alright. That's really all there is to it. And the next thing you might see, the other kinds of questions you might see, is you might actually have to go backwards. And what I mean by that is you might have to go from scientific notation out back into standard form. So you might have to rewrite scientific notation numbers as normal numbers. So let's get a few examples. I'm going to show you a really simple process for doing that too. So imagine we wanted to take this number here, and we want to write it as a normal number. Well, really all you're going to do here is the exponent is just going to be the number of decimal places that you moved, just as it was up above, and if the exponent is positive, your number becomes larger. If it's negative, it becomes smaller. So, for example, 5.45×108. This 8 here means move the decimal place. In order for the number to become larger, you're going to have to move it to the right. So 5.45, what you do is you take this number, and you're going to shift it to the right 8 times1, 2, 3, 4, 5, 6, 7, 8, and you're going to fill in 6 zeros over here. So this is how this number would be in standard form. And for this last one, 9.62×10-5. So what we're going to do is 9.62, and the exponent is the number of decimal places you'll move. And if the exponent is negative, your number becomes smaller, so you're going to have to shift to the left. So you're going to go 1, 2, 3, 4, 5, and then fill in your zeros. 1, 2, 3, and 4. Your decimal place ends up over here, and you're going to put another 0 there. So that means that this here is how you would expand the scientific notation back out to a normal number. Alright, guys. That's all there is to it.

Rewrite 0.00016 kg in scientific notation.

• A. 1.6×10^-4
• B. 16×10^-3
• C. 1.6×10⁴
• D. 1.6×10^-3

Rewrite 299,800,000 m/s in scientific notation.

• A. 2.998×10⁵
• B. 3.00×10⁸
• C. 3.00×10⁵
• D. 2.998×10^-5

Rewriting in Scientific Notation

Hey, guys. We're going to take this number here, and we're going to express it in scientific notation. Now, you might be a little confused at first because you might think, well, this already looks like it's in scientific notation. But the problem is that our scientific notation format is a number 8.bc, in which this number is between 1 and 10 times 10d. So the problem is that this number here isn't really in the right format. So we're going to take this number and we're going to express it in the correct format. Here's how we can do this: We take this number that's in this weird kind of scientific notation, and we could just write it out as a normal number and then recompress it back into scientific notation. Here's how we do that. We take this number 0.0000529 × 106 and we want to decompress or we would actually kind of expand this out into a normal number again. So we follow the rules for converting numbers into standard form. We'd look at the exponent, which tells us how many decimal places to move. The negative means that we're going to end up with a number that is much less than 1. So that tells us which way to move the decimal point. We move it to the left 6 times, filling in the zeros. So, our decimal point actually ends up over here. This ends up being 10 zeros before. Now, this is our actual number here in terms of standard form. Now, I want to take this number and recompress it back into scientific notation. We move the decimal so that we get a number between 1 and 10. After moving 11 decimal places, it becomes 5.29 × 10-11, which is our answer in scientific notation. It's in the correct form where this is a number between 1 and 10. So that's it. You guys can just move on to the next video. But if you want to stick around, I'll show you a really quick, sort of a shortcut way to do this. From the original number, we can figure out how to get to this number really quickly. So what we do is we go from the decimal place, which is over here, until we get a number that's between 1 and 10, so 5.29. If you do that, you're going to move 5 decimal places here in order to get to this number. Now what happens is that because we're going from a number that is much less than 1, this 5 actually means a negative 5 in the exponent. So if you take this negative 5 and this negative 6 and you kind of add them together, then you'll actually get this negative 11. So that's a shortcut way to do this. All right, guys. That's it for the

Rewrite 3.41 × 10⁻⁴ in standard form:

• A. 0.000341
• B. 34,100
• C. 0.0000341
• D. 3,410

Rewrite 9.98 × 10⁷  in standard form.

• A. 0.000000998
• B. 0.0000000998
• C. 9,980,000,000
• D. 99,800,000

Here’s what students ask on this topic:

What is the SI system of units and why is it important in physics?

The SI system of units, or the International System of Units, is a standardized system used globally for scientific measurements. It includes base units like kilograms (kg) for mass, meters (m) for length, and seconds (s) for time. This system is crucial in physics because it ensures consistency and compatibility in measurements and calculations. For example, in the equation for force, $F=ma$, all units must be compatible (e.g., Newtons, kilograms, meters per second squared) to yield accurate results. Using a standardized system like SI helps avoid errors and facilitates clear communication among scientists worldwide.

How do you convert between different metric prefixes in the SI system?

To convert between different metric prefixes in the SI system, follow these steps: First, identify the starting and target prefixes. For example, converting from kilometers (k) to meters (m). Next, determine the power of 10 associated with each prefix (e.g., kilo is 10³). Calculate the difference in exponents between the starting and target prefixes. Finally, shift the decimal point in the original number by the number of places equal to the difference in exponents. For instance, converting 5 kilometers to meters involves moving the decimal 3 places to the right, resulting in 5000 meters.

What are metric prefixes and how are they used in physics?

Metric prefixes are symbols that represent specific powers of 10, used to simplify large or small numbers in the SI system. Common prefixes include kilo (k) for 10³, milli (m) for 10^-3, and micro (μ) for 10^-6. These prefixes are attached to base units to form more manageable numbers. For example, 5 kilometers (km) is 5000 meters (m), and 4.6 milliseconds (ms) is 0.0046 seconds (s). Using metric prefixes helps avoid writing lengthy numbers and makes calculations more straightforward.

How do you convert a number from standard form to scientific notation?

To convert a number from standard form to scientific notation, follow these steps: First, move the decimal point to create a number between 1 and 10. For example, converting 304000 to scientific notation involves moving the decimal 5 places to the left, resulting in 3.04. Next, count the number of places the decimal was moved; this becomes the exponent of 10. If the original number is greater than 10, the exponent is positive; if less than 1, the exponent is negative. Thus, 304000 becomes 3.04 × 10⁵.

Why is scientific notation useful in physics?

Scientific notation is useful in physics because it allows for the concise representation of very large or very small numbers, which are common in scientific calculations. For example, the mass of the Earth is approximately 5.97 × 10²⁴ kilograms. Writing this in standard form would be cumbersome and prone to errors. Scientific notation simplifies calculations, improves readability, and ensures precision, making it an essential tool for physicists.