Converting Numbers to Scientific Notation

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  • 0:05 Scientific Notation
  • 1:36 Converting to…
  • 3:09 Example 1
  • 3:45 Example 2
  • 4:24 Lesson Summary
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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.

Scientific Notation

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.

Converting to Scientific Notation

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.

Example 1

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

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