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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to convert any number you come across into scientific notation. You will also learn why scientific notation is used and where you are most likely to see it.

In this video lesson, we are going to take a look at **scientific notation**. This is a special way to write numbers. Who uses scientific notation? If you guessed scientists, you are 100% correct! Scientists use it because it is a way to write out really large and really small numbers without having to write a whole bunch of zeroes.

What does it look like? You will know that you are looking at scientific notation when you see a number multiplied by 10 to a power. For example, 2.7 * 10^3 is the number 2,700 written in scientific notation. See the multiplication by 10 to a power? We'll see later how we get the number of the power. Another example is 2.7 * 10^-3, which is the number 0.0027 written in scientific notation.

While it's easy for us to write and read 2,700 and 0.0027, when we get to much larger numbers, scientific notation makes it much easier to write them. For example, instead of writing 1,988,000,000,000,000,000,000,000,000,000, we could just write 1.988 * 10^30. Doesn't that look much neater? This really large number is actually the mass of the sun in kilograms.

It's quite easy to convert our regular numbers into scientific notation. Let's convert the number 3,400,000 into scientific notation. First, we write out the first few non-zero digits and place a decimal after the first digit. We have 3.4. Now, we're going to count how many digits there are after the 3. We have 6. This tells us that our power is 6. So, we finish off by writing 3.4 * 10^6. This tells us that we have a total of 6 digits after the 3. We would add zeroes until we have a total of 6 digits after the decimal.

If our number is smaller than 1, our scientific notation will have a negative exponent. Let's convert the number 0.00041 into scientific notation. This time, instead of taking the first few non-zero digits, we are now taking the last few non-zero digits and placing a decimal after the first non-zero digit. We have 4.1. Now, we count the number of digits away from our beginning decimal. We get 4. So, this tells us that our power is -4. Our scientific notation, then, is 4.1 * 10^-4.

Another way you can remember whether the power is positive or negative is by the direction you need to move the decimal point. If you need to move it to the left, then your power is positive. If you need to move it to the right, then your power is negative. Let's look at a couple more examples.

*Convert 6,800,000,000 into scientific notation.*

We begin by writing our first few non-zero digits with a decimal point after the first digit. We get 6.8. Now, we count how many digits we have to move our beginning decimal point to get to the 6.8 spot. We have to move the decimal to the left, so our power is positive. We count 9 spaces, so our power is 9. Our scientific notation, then, is 6.8 * 10^9.

*Convert 0.0000056 into scientific notation.*

This time, our number is smaller than 1. So, we write the last few non-zero digits and place a decimal point after the first non-zero digit. We get 5.6. Again, we count how many digits we have to move the decimal to get to the 5.6 location. We have to move the decimal to the right, so our power will be negative. We count 6 spaces, so our power is -6. Our scientific notation, then, is 5.6 * 10^-6.

Let's review what we've learned. We learned that **scientific notation** is a special way scientists use to write very large and very small numbers. You will see some non-zero digits with a decimal place after the first digit multiplied by 10 to a certain power. This power tells you how many digits to move the decimal to get to your number.

To convert any number into scientific notation, you write the non-zero digits, placing a decimal after the first non-zero digit. Then, you count the number of digits you need to move the beginning decimal to get to where your decimal is now. If you move the decimal to the left, then your power is positive. If you move the decimal to the right, then your power is negative.

After you've reviewed this video lesson, you should be able to:

- Define scientific notation and recall why it is used
- Explain how to convert any number to scientific notation

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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