## Transcript

Title text reads, The Mysteries of Life with Tim and Moby. Moby is looking through a telescope. A view of the night sky fills the screen, with a bright reddish spot in the center. Moby turns to Tim and beeps.

TIM: How far away is Mars? I'm not sure. It's really far.

On-screen, a letter appears. Text reads as Tim narrates:

Dear Tim and Moby, What is scientific notation? From, JJcat.

TIM: Scientific notation is a way of writing numbers using powers of ten. It comes in handy when you're dealing with really big or really small numbers.

Moby beeps. Tim opens a book.

TIM: Well, according to this space almanac, it looks like Mars is about 59 million kilometers away from the earth right now. When you see a number like 59 million written out as 5 9 0 0 0 0 0 0, that’s standard notation.

On-screen, the number, 5 9 comma 0 0 0 comma 0 0 0, appears. A label appears, reading, standard notation.

TIM: Like I said, in scientific notation, numbers are expressed as a power of 10, multiplied by a number whose absolute value is less than 10 but greater than or equal to 1.

Moby looks confused. He beeps.

TIM: Well, maybe the best way to explain is to just convert our number, 59 million, to scientific notation and let you see for yourself.

Moby's chest plate slides open and reveals two display screens. The first is labeled, standard notation, and displays the number, 5 9 0 0 0 0 0 0, followed by a decimal point. The second is labeled, scientific notation, and displays a blank space, followed by the symbols, times 10 to the x, power.

TIM: We start by converting our standard notation number into a number whose absolute value is less than 10 but greater than or equal to 1. We do this by dividing the number by 10. Remember that when you divide a number by 10, you move the decimal point one place to the left. It might help to keep track of the number of places you move the decimal point.

On-screen, the decimal point on the standard notation display moves to the left, one place at a time. A decimal counter marks the number of places the point moves: 1, 2, 3, 4, 5, 6. The display now reads, 59.000000, and the decimal counter reads, 6. Moby beeps.

TIM: Nope. 59 is still too big. Remember, we need a number that is less than 10 but greater than or equal to 1.

On-screen, the decimal point moves one more place to the left. The display now reads, 5.9000000, and the decimal counter reads, 7.

TIM: There you go. Now, to complete the scientific notation, we need to show that this number, 5.9, is being multiplied by some power of 10.

On-screen, 5.9 appears in the blank space on the scientific notation display. The display now reads, 5.9 times 10 to the x, power.

TIM: What we're really doing here is undoing the division.

Moby beeps.

TIM: Okay, when you multiply a number by 10, you move the decimal point one place to the right. So how many times will you have to multiply the number 5.9 by 10 to make it equal to 59 million?

Moby beeps.

TIM: Right. 1, 2, 3, 4, 5, 6, 7. 10 to the power of 7.

On-screen, the decimal point on the standard notation display moves to the right 7 times, back to where it began. The display now reads, 5 9 0 0 0 0 0 0.

TIM: There. 5.9 times 10 to the seventh.

On-screen, the x, on the scientific notion display changes to a 7. The display now reads, 5.9 times 10 to the seventh.

TIM: You'll notice that 7 is the number of places we moved the decimal point in the first place. Using negative exponents, we can also put really small numbers into scientific notation. Here's a really small number: 0.000031.

On-screen, Tim holds up a sign reading, 0.000031.

TIM: We move the decimal point over to get ourselves a number that's less than 10 but greater than or equal to 1.

On-screen, the number, 0.000031, appears on the standard notation display in Moby's chest. The scientific notation display resets to a blank space, followed by, times 10 to the x, power. On the standard notation display, the decimal point moves 5 places to the right. The display now reads, 0 0 0 0 0 3 point 1.

TIM: Since we moved the decimal point to the right, and we're trying to show that our number is being made smaller, and not larger, our exponent is going to be negative.

On-screen, an arrow appears on the standard notation display, pointing to the right. The decimal counter marks the number of places the decimal point moves: negative 1, negative 2, negative 3, negative 4, negative 5.

TIM: In scientific notation, this would be 3.1 times 10 to the negative fifth, since our decimal point moved five places to the right.

On-screen, 3.1 appears on the scientific notation display, and the x, changes to negative 5. The display now reads: 3.1 times 10 to the negative fifth.

TIM: For any number greater than 0 but smaller than 1 represented in scientific notation, the exponent will be negative. And that's scientific notation. It may not seem immediately useful, but you'll be glad you know it if you ever have to deal with really really huge numbers, or really really small numbers.

Moby beeps as he looks through the telescope.

TIM: Martians? How can you possibly see Martians? That telescope's pretty weak, and Mars is 59 mill, ah, 5.9 times 10 to the seventh kilometers away.

Moby beeps.

TIM: Of course I'm right. Besides, there aren't any Martians to see. I'm gonna go make a sandwich. You want one?

Moby stares out the window as Tim walks away. Moby beeps.

TIM: Two? What are you gonna do with two sandwiches?

On-screen, Moby waves to a friendly green alien right outside the window.