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Express the following numbers in scientific notation:(a) $0.000000027,$ (b) $356,$ (c) $47,764,$ (d) $0.096.$

a $2.7 \times 10^{-8}$b $3.56 \times 10^{2}$c $4.7764 \times 10^{4}$d $9.6 \times 10^{-2}$

Chemistry 101

Chapter 1

Chemistry: The Study of Change

Intro to Chemistry

Carleton College

Drexel University

University of Maryland - University College

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 just asking you to express these numbers and scientific notation that they give you So first, let's go over. What scientific notation is Simon ships? Scientific notation is basically just a notation where you move the decimal 0.2 after two after the first digit and before the 2nd 1 So, um and you multiply that number by 10 to the whatever power to kind of get it to whatever value want it to be. So to make that more clear, let's go over the first question and kind of walk through this together. So, like I said, scientific notation is where you want to get the decimal point after the first digit and before the 2nd 1 So we kind of as you can see, we kind of move it as point point here, right? But as you can see, these two numbers are not equal right. 0.27 is not equal to 2.7. Right? So we need a multiply this number by something to get it equal to this side. Right? So what are you going to do? We're gonna have to multiply by 10 to the something power. Right? And how do we know that power? How do we know that exponents? Well, we have to count the decimal points. Right? Count how much it moves to get to 2.7 and multiplied by that. Right? So let's count it. We have one, 2345678 It has moved eight spots to the right to get to 2.7. And since moving to the right, it's negative. So 10 to the 10 to the negative 82.7 times tend to the Nate eight. Eat Negative. A equals this number over here. Okay, so let's go over another one. We have 3 56 So again, we want to move the decimal 560.2 right after that first number. So 3.56 Now, how do we have to multiply this by to get it equal? We have to counter decimals, right? And this time, since the decimal needs to move to the left, we're gonna have a positive value for exponents is gonna be 12 okay to get it to 3.56 So it's 10 times 10 to the two. And the reason why it's positive is because we need to increase 3.56 to get to 3 56 right, whereas in the 1st 1 we would have to decrease 2.7 to get to 0.0 whatever. 2.7, right? So that's how to do this one. And the next question similar to the last question. You're still you're going to do with positive numbers here because greater than one, we're gonna 4.7764 times 10 to the something right. So now we need to count it again. Kept the decimal points. 12344 Right, so that we could get it to 4.764 point 7764 and it's 10 to the fourth. And it's positive because we need to increase this number to get to this number. Okay, and now we have our last problem here. It's similar to the 1st 1 as, and it's gonna be a negative because it's less than one. So we got what 9.6 times tend to the something we don't know what it is yet. Um, this counter decibels we're gonna move it to the right. So it's me one, then two more decimal right here, right? And since we're moving into the right, it's negative. So 10 to the negative two. So 9.6 times 10 to the negative, too. I hope this is helpful and helping you understand on scientific notation because very, very useful. And it's very important in just science in general. So yeah, thanks for listening.

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