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Matter and Measurements

Scientific notation is used to turn small or large inconvenient numbers into manageable ones.

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Scientific Notation

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Oftentimes when we deal with calculations and chemistry, we're gonna run into the situation where we're dealing with extremely large numbers and extremely small numbers, not convenient way to deal with. This is scientific notation. Now scientific notation is used to turn these small or large inconvenient numbers into manageable ones. So here we have an example of something written in scientific notation. We say it's 6.88 times 10 to the negative power. Now what's in red is called our coefficient. Now the coefficient is just the beginning, part of the value that is equal to or greater than one, but less than 10. Next, we have our base, which is here. This is the portion of the scientific notation value that is always 10. So that number is always gonna be 10 if we're writing something in scientific notation. And then finally the exponents, which we sometimes called the power. This is the number of places the decimal must was moved to create the scientific notation value. Now we'll talk about in a couple of videos. What happens when it's positive versus negative? What effect does that have on my value overall Now, another important thing when it comes to this exponents is that it must be expressed as a whole number. Integer So negative. 12 Positive three. Negative to can't be decimals or fractions. Must be whole numbers. Now that we know the basically out of scientific notation, click on the next video and let's take a look at the example question.

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Scientific Notation Example 1

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So now that we know the major parts of scientific notation, let's put it to practice with this example question here it says Which of the following scientific notation values is written correctly. So if we take a look at a here, we have 1.25 times 10 to the negative 1/4. Well, if we look the coefficient, this part here is fine. It's a number between one and 10. Here are base is 10. But our error is that the exponents is not a whole number integer It's negative 1/4. This is not written correctly. Next, if we take a look at the very beginning we see that our coefficient here is a number that is not between one and 10. This is not allowed for scientific notation. The base is correct and the exponents is a whole number. But again, the coefficient is not a number between one and 10. So this will not work for see, we have our co efficient with which is a number between one and 10. So this is allowed. Our base is 10 and our exponents is ah whole number integer three. So this is a correct way off writing something within scientific notation values. So this is our answer. If we look at D, though, for Dean are coefficient again is a number between one and 10, but our base here, our base is not 10. It's to remember if you're writing something in scientific notation. The base is always 10. The exponents is correct, but it's the base that's making an incorrect overall. So again, remember the three components of scientific notation and the limits that they each have following that, in truth, that you write scientific notation correctly every time.

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Scientific Notation

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Now that we know about scientific notation, it's going to become important on how to convert from scientific notation to standard notation. Now, standard notation itself is just the normal way of writing numbers. Okay, so here, in order to go from scientific notation to standard notation, it all deals with looking at the exponents. Now, we're gonna say here that a positive exponents tells you to make the coefficient value larger. So if we take a look here, we have 7.17 times 10 to the five here. Five is telling me that I need to make the coefficient larger by five. So we're starting out with 7.17 to make it larger. I'm gonna move the decimal place over to the right, so we have to move it. Five spaces. So So our new way of writing this would be 717 comma 000 So this becomes 717,000 as our new value. Now, what if the exponents is negative? Well, a negative exponents tells you to make the coefficient value smaller, So if we take a look here, this is negative. Seven So we have 3. We need to make this number smaller, so we're gonna have to move it to the left and we move it over seven spaces. So So that's gonna be point 000003 to 5. So these values here would represent the normal way of writing numbers. Now it's inconvenient because you can see how much writing is involved in writing both of these numbers. And if our exponents were even bigger, positive or even more negative value that beam or movement of the decimal. That's the whole point of scientific notation. It changes these inconvenient, non manageable numbers into something that's easier for us to read. Now that we've done this, click on the next video and let's take a look at the practice question. When we put this into practice, remember, look at the exponents to determine if you wanna make the coefficient larger or smaller.

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Problem

Convert the following scientific notation values into standard notation.

a) 1.25 x 10^{-4}

b) 3.20 x 10^{-9}

c) 1.6100 x 10^{4}

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Scientific Notation

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Now we're going to take a look at How exactly do we change standard notation into scientific notation? Now, the key is to look at the coefficient. Now, we're gonna say to convert a number into a scientific notation value, make sure the coefficient is equal to or greater than one, but less than 10. So what we learn the very beginning of scientific notation is the key to changing standard notation into scientific notation. So if we take a look here, we're gonna say increasing the coefficient makes the exponents value decrease. All right, so here we have a number of 0.145 We need to make sure that that coefficient, which we're going to make, has to fall between one and 10. Here is our decimal place. We're gonna have to move it. spaces so that we can get 1.45 which is a value between one and 10 now. We made the coefficient larger since we made the coefficient larger. That means the exponents has to become smaller, so the coefficient increased by five. So the exponents has to decrease by five because they're opposites of one another. Now, decreasing the coefficient value makes the exponents value increase. So here in this one, there is. We could think of there being a decimal point there, and we're gonna move it over enough spaces in order to make this coefficient a number between one and 10. So we're gonna move. One, aN:aN:000NaN spaces. So that becomes 1.13 to times 10. Now, we moved over eight spaces in order to make this smaller. So if the coefficient is decreasing by eight spaces, that means our exponents has to be increasing by eight spaces. So it'll be a positive eight here. So that would be the scientific notation value for this number here. Later on, we'll talk about things such a significant figures which will help us to even simplify this scientific notation, even mawr, because there's an awful lot of zeros here at the end. But for now, this would be the entire value that we place to show that we moved decimal place eight spaces over to make the coefficient smaller and thereby increasing the exploding by eight. Now that we've seen these examples move on to the practice question left at the bottom of the page

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Problem

Convert the following standard notation values into scientific notation.

a) 377,000

b) 0.000101

c) 707.82

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