Question

Scientific Notation
Video Player
00:0003:26
None
Captions

Show Transcript
Education Galaxy presents. Scientific notation. Today, we will explore how to represent numbers that are very large, like the diameter of Saturn are very small like the diameter of a human hair in scientific notation. We will begin by looking at the format of a number written in scientific notation. Then we will learn how to convert a number from standard notation to scientific notation And finally, we will learn how to convert a number from scientific notation back to standard notation. Let's look at the format for scientific notation You have to have one non zero digit, a decimal point, the rest of your digits, a times ten, and then a power. Or an exponent. Look at these numbers. Do you see any that are in scientific notation? These two numbers fit the format for scientific notation So what's wrong with these numbers? This one's just totally wrong. This number has a zero and then the decimal point. You have to have one non zero digit and then the decimal point. This number has two digits and then the decimal point. Let me show you how to take a number that is in standard notation and rewrite it in scientific notation. We need to think of numbers in two different categories, numbers that are less than one, and numbers that are greater than one. As I look at the number left to right, four is my first non zero digit. So I'm going to write four decimal point, the rest of the digits, six seven times ten. And since the number in standard notation is less than one, I need to have a negative exponent Now, we simply need to count how many places a decimal moved. One, two, three, four, five. When I have a number greater than one, I write the first non zero digit, the decimal point, then the rest of the digits note I don't put another decimal point. I say times ten, and we need to count how many places the decimal moved. It's two. Now let's go the other direction. Let me show you how to take a number that is written in scientific notation and rewrite it in standard notation. We'll start with the decimal portion of the number. Since the exponent is negative, we're going to move our decimal point to the left. In this case, we'll move it left five times. One, two, three, four, five. Fill in with zeros. A zero to the left of the decimal is optional. Anytime the number in scientific notation has a negative exponent, our number will be less than one. Let's try another one. We'll start with the decimal portion of the number Since it's a positive exponent, we will move our decimal point to the right and we'll move it right four times. One, two, three, four. Once again, fill in with zeros who are needed. Since this number is a whole number, you don't have to put the decimal point at the right. Anytime the exponent on the number in scientific notation is positive, you will end up with a number that is greater than one. We use scientific notation to represent numbers that are very large. Our numbers that are very tiny and to focus on the significant digits. Now, you're ready to try some problems on your
Close
The mass of a hummingbird egg is
grams.

How is this number written in scientific notation?

A
B
C
D
The mass of your little “pinky” toe is about
.
How is
written in scientific notation?
A
B
C
D

Answer 1

I don’t see the actual numbers or the answer choices in your message. Could you paste the two numbers (and the multiple-choice options) here or attach a screenshot? Then I’ll convert them and pick the correct choices.

While you paste them, here’s a quick reminder of the method so you can follow along:

How to convert from standard notation to scientific notation
- Put the number in the form: one nonzero digit, a decimal point, the remaining digits × 10^n.
- If the number is ≥ 1, move the decimal left until only one nonzero digit is left before the decimal; n is how many places you moved (positive).
- If the number is < 1, move the decimal right until you reach the first nonzero digit; n is the negative of how many places you moved.

Examples
- 0.0000467 → move decimal right 5 places → 4.67 × 10^−5
- 46,700 → move decimal left 4 places → 4.67 × 10^4

How to convert from scientific notation to standard notation
- If exponent is positive, move decimal right that many places (fill with zeros as needed).
- If exponent is negative, move decimal left that many places (fill with leading zeros as needed).

Send the specific numbers/options and I’ll give the exact answers.