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Express the answers to the following calculations in scientific notation:(a) $145.75+\left(2.3 \times 10^{-1}\right)$(b) $79,500 \div\left(2.5 \times 10^{2}\right)$(c) $\left(7.0 \times 10^{-3}\right)-\left(8.0 \times 10^{-4}\right)$(d) $\left(1.0 \times 10^{4}\right) \times\left(9.9 \times 10^{6}\right)$

a. $145.75+\left(2.3 \times 10^{-1}\right)=145.75+0.23=1.4598 \times$ $10^{2}$b. $\frac{79500}{2.5 \times 10^{2}} \times \frac{7.95 \times 10^{4}}{2.5 \times 10^{2}}=3.2 \times 10^{2}$c.$\left(7.0 \times 10^{-3}\right)-\left(8.0 \times^{-4}\right)=\left(7.0 \times 10^{-3}\right)-(0.80 \times$ $\left.10^{-3}\right)$d. $\left(1.0 \times 10^{4}\right) \times\left(9.9 \times 10^{6}\right)=9.9 \times 10^{10}$

Chemistry 101

Chapter 1

Chemistry: The Study of Change

Intro to Chemistry

Alya A.

August 26, 2021

Determine the number of significant figures in each of the following measurements: (a) 2901 g (b) 4867 mi (c) 60,104 ton (d) 40.2 g

Rice University

University of Toronto

Lectures

02:29

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry deals with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds. Chemistry also involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications.

04:42

In chemistry and physics, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles and objects that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states (known as phases) that are defined by various physical properties, such as state of matter, phase, shape, and density. The Standard Model of particle physics and the general theory of relativity describe fundamental particles and the fundamental forces acting between them that control the structure and dynamics of matter.

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Hi. So this question is asking you to do the falling calculations and express the answers in scientific notation. And, of course, as as with all mathematical calculations, when you express a scientific notation or just with any answer, actually you want to tap the correct number of significant digits. So we're also gonna try to account for that as well. So let's look at the first question. Here we have 1 45.75 plus open parentheses, 2.3 times 10 to the negative, one close parentheses. So here we want to, um God, you wouldn't do what is in the premises first. So 2.3 times 10 to the negative one. So when you want to fly by something that is to the power of negative one, your decreasing that number right, it's smaller than it. It's gonna become smaller. So since it's 10 words going through the decimal point one to the left because we're making smaller and of course I'll be 0.23 So we got one 45 175 175 plus zero point to street. Okay, and this comes out to course, we just do the addition. There will be 1 45 months. 98 Now, as you can see, we didn't round anything. But that's because when we do addition, right, we look at the least number of decimals and we rounded that number. But since both of our Adan's here have the same number of decimals A. So you can see why two decimals years 75 and then two decimals here to three. We have We only need two decimals in the end. The answer. So we don't throw out anything. But now let's convert it to scientific notation. So the 1.45 98 Now that is the general notation. But we're now we multiply it by something right? Most of by tens of this something power. What power should that be? What power do we need? A Multiply this number. This number here. Sorry. This number here To get to this number, we need to multiply this by 100 right? Because two decimal points to the left or to doesn't point to the right from this one, and we'll get to this one. So, um, times 10 to the second power. Because hundreds. So 1.4598 times 10 to the second power. Now, let's look at this second question here we have 79,500 divided by Oprah theses 2.5 times 10 to the too close parentheses. So, um, for this one is different than the last question. Because the last question we wanted to do it was in the parentheses first, right? But here we asked, you don't want to simplify, because when you do division, you want to convert everything to scientific notation because then you can cancel out a lot of the 10 powers that are in the question. So what I mean by that is I'm gonna give you example here at the bottom. Um, let's see, I simplified to one times 10 to the to over one times 10. Right Now, I see this is very easy to cancel out because you can see I have tend to the two on top and 10 on the bottom so I can just cancel this out, and then the top just becomes 10 right? And the bottom is still one. So because of that, we want to come for everything is not rotation. So we can cancel numbers. So back toe, the question was, convert the top number 79,502 sides of rotation. So it seven point 95 times 10 to the four over. Still 2.5 times 10 to the to. And we're gonna cancel this one out. Just one just becomes the bottom. What is just gone. But the 2nd 1 is reduced to two to power, and we just plugged store calculators of 7.95 times 10 to the to divided by 2.5. And you should get three. 18 now. Um, as you can see, you want Teoh. All right, so I'm gonna do this in going to do this in a scientific notation. Since we already know what's gonna be so three point one age times 10 to the to now, we actually I'm done here. We actually do a round it. Why? Because let's look at our at our first part here. What's the least significant digits here? The bottom of the one where we have to significant digits 2.5. And the answer right now has three. So we need around it to two significant figures. So we're gonna round it to this place. Right? This place right here. So we actually 3.2 times 10 to the cheer, so I answer. Okay, so pretty simple. Look at our next one. We have seven, um, 0.0 times, 10 to the negative. Third, minus 8.0 times. 10 to negative fourth. Now here. What we want to do is you want to convert these two numbers into the same, um, unit of scientific notation. So what I mean by that is this is this first number is done with respect to 10 to the negative. Third, this one has done with respect to tend to the negative fourth. So it would be easier here is to make this one here. This number, the second number with respect to tend to the negative thirds that we can just, you know, subtract them and just keep the 10 to the negative third. Okay, So it's almost like we're moving the decimal point to the same place so that we can subtract them. Normal. Okay, so let's convert that second number to 10 to the negative Third. You'll see what I meant by what I just said in little second. Um, so if you want to convert this 10 to negative third, we have to move the decimal place to the left. Right, So we're going to do Ah, zero points eight times 10 to the negative third. Now, as you can see, um oh, well, we really have to do is just attracted these two numbers here. And then we can just keep the 10 to the negative third in our answer, and it's already gonna be in scientific notation. So seven, my A zero point. Oh, just six point. Oh, sorry. Actually, for this for this answer right here, it's still gonna have to sing every conditions so six point to times 10 to the negative. Third says Perfect day, Two significant digits. And we didn't really have to convert anything is active in irritation because it was already insect identification. It's pretty nice now for this next question. OK, so this is actually easier than the other question we've done so far because you can pretty much just multiply everything together and it's gonna be too significant digits. And it's basically still gonna be in, um, and still would be in scientific notation. We need adjusting because this first numbers once. So this isn't going to really change too much. Um so basically, just plug everything in together and multiply it. It should get out to 10 or 9.9 times 10 to the 10. Okay, so this is actually the easiest one by far. Just a lot of plugging tricot. Great. So, um yeah, significant digits and sanitation is, and it's very important, just math and science in general. So, um, it's very important for you to get this down and hope this was helpful and allowed you to understand things a little better. Thank you.

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