Scientific Notation to Standard Form (Small Numbers) | Math with Mr. J

Welcome to Math with Mr. J. In this video, I'm going to cover how to go from scientific notation to standard form. And we will specifically be working with negative exponents in this video, so small numbers. Now remember, scientific notation is a way for us to write really large numbers or really small numbers in a shorter, more condensed way. So we're going to start with scientific notation, and go to standard form, which standard form is basically how we typically think of numbers and write numbers. Let's jump into our examples, starting with number one, where we have eight times 10 to the negative sixth power. Let's write this in standard form. All we need to do here is check the exponent and move the decimal. So let's see what this looks like. We'll start by writing eight off to the side. So we're taking what's to the left of the multiplication sign. So we have eight, and then we need to include the decimal, which comes after a whole number, so to the right of the ones place, so right here. Now we need to take a look at our exponent, which is negative six. That tells us we moved the decimal six places. But which way, do we move it left or right? Just remember, when we have a positive exponent, we know that we are working with a large number. When we have a negative exponent, we know that we are working with a small number. Well, we have a negative exponent here, so we are working with a small number. That means we move the decimal to the left. We are multiplying eight by 10 to the negative sixth power. Eight is going to be decreasing in value here. So let's move the decimal six places to the left. So one, two, three, four, five, six. And then we can fill those gaps, those places, with zeros. So a zero here, here, here, here, and here. And that's our standard form. But let's rewrite this a little neater without the decimal movement underneath. We will start with a zero, and then the decimal, and then one, two, three, four, five zeros, and then the eight. So one, two, three, four, five zeros, and then the eight. And we're done. That's our standard form for number one. Let's move on to number two, where we have 2.74 times 10 to the negative eighth power. Let's start by writing 2.74 off to the side here. And then taking a look at the exponent, we have negative eight. Since we have a negative exponent, that tells us we have a small number here. And we need to move the decimal to the left. And we're going to move it to the left eight places. So one, two, three, four, five, six, seven, eight. And now we can fill those places with zeros. And that is our standard form. So let's rewrite this. So zero, then the decimal, then we need one, two, three, four, five, six, seven zeros, and then 2.74. So one, two, three, four, five, six, seven, and then 2.74. And that's our standard form for number two. Lastly, let's move on to number three, where we have 1.6 times 10 to the negative 11th power. Let's start with 1.6 off to the side here. So 1.6, and then we have an exponent of negative 11. So a negative exponent here, that tells us we have a small number, and we need to move the decimal to the left. And we're moving it to the left 11 places. So one, two, three, four, five, six, seven, eight, nine, 10, 11. And now we need some zeros. So let's fill those gaps, those places, and that will give us our standard form here. And let's rewrite this. So we have zero, and then the decimal, then we need one, two, three, four, five, six, seven, eight, nine, 10 zeros, and then 1.6. So one, two, three, four, five, six, seven, eight, nine, 10. And those are all of our zeros. Then we need one, six. And that's our standard form for number three. So there you have it. There's how to go from scientific notation to standard form. I hope that helped. Thanks so much for watching. Until next time, peace.