Uploaded by 1veritasium on 02.02.2011

Transcript:

In science, we often have to deal with some very large numbers. For example, the mass

of the sun.

That is the mass of the sun. Two followed by thirty zeros in units of kilograms. That

is two thousand billion billion billion kilograms. There has got to be a better way to write

that. Can you imagine if there wasn't? And so we find that the mass of the sun is two

zero zero zero zero zero zero zero zero zero. Yes? Sorry could you repeat that? I was with

you up to two zero zero zero zero zero? Ahh? It was ahh... two zero zero. So to represent

large numbers easily, we use something called scientific notation. Scientific notation takes

advantage of powers of ten. For example, ten to the power of two means take two tens and

multiply them together. And you get 100. Ten to the power of three means multiply three

tens together. And you get 1000. Ten to the power of four means take four tens and multiply

them together. And you get 10,000. So you should notice a pattern developing. When it's

ten to the power of two, our final answer has a one followed by two zeros. Ten to the

power of three, our final answer has a one followed by three zeros. Ten to the power

of four, again, four zeros. So if we wanted to represent the mass of the sun in scientific

notation, we would need thirty zeros. So we represent that using ten to the power of thirty.

This means that we're multiplying ten by itself thirty times, which gives us a one followed

by thirty zeros. But the mass of the sun is actually twice that. It's two followed by

thirty zeros so we can multiply two by ten to the thirty in units of kilograms and that

is the mass of the sun. It's much easier to write and it takes up much less space on the

page. The other problem is we have to deal with some tiny numbers. For example the mass

of a proton is...

That is the mass of a proton. Zero point, and there there are 26 zeros, and then 1673

kilograms. A truly tiny number so how do we deal with this? Well again it's using a similar

trick. If we raise ten to the power of minus one, it means divide by ten, not multiply

by ten. So this means divide by ten which gives you zero point one. Ten to the power

of minus two means divide by ten twice, which gives us zero point zero one, a hundredth.

Ten to the power of minus three means divide by ten three times, or zero point zero zero

one. So again you see a pattern developing. The exponent here tells you how many places

to the right of the decimal that the one is. So in this case, ten to the minus two, the

one is two places to the right of the decimal. Here, ten to the minus three, the one is three

places to the right of the decimal. So in this case I actually have a one that is 27

places to the right of the decimal. So I can write the mass of a proton as 1.673 times

ten to the minus 27 kilograms. And this ten to the minus 27 has the function of putting

this number, 1.673, 27 decimal places to the right of the decimal point. So as a challenge

question to see if you've understood it: if the sun were made entirely of protons, how

many protons would there be in the sun?

of the sun.

That is the mass of the sun. Two followed by thirty zeros in units of kilograms. That

is two thousand billion billion billion kilograms. There has got to be a better way to write

that. Can you imagine if there wasn't? And so we find that the mass of the sun is two

zero zero zero zero zero zero zero zero zero. Yes? Sorry could you repeat that? I was with

you up to two zero zero zero zero zero? Ahh? It was ahh... two zero zero. So to represent

large numbers easily, we use something called scientific notation. Scientific notation takes

advantage of powers of ten. For example, ten to the power of two means take two tens and

multiply them together. And you get 100. Ten to the power of three means multiply three

tens together. And you get 1000. Ten to the power of four means take four tens and multiply

them together. And you get 10,000. So you should notice a pattern developing. When it's

ten to the power of two, our final answer has a one followed by two zeros. Ten to the

power of three, our final answer has a one followed by three zeros. Ten to the power

of four, again, four zeros. So if we wanted to represent the mass of the sun in scientific

notation, we would need thirty zeros. So we represent that using ten to the power of thirty.

This means that we're multiplying ten by itself thirty times, which gives us a one followed

by thirty zeros. But the mass of the sun is actually twice that. It's two followed by

thirty zeros so we can multiply two by ten to the thirty in units of kilograms and that

is the mass of the sun. It's much easier to write and it takes up much less space on the

page. The other problem is we have to deal with some tiny numbers. For example the mass

of a proton is...

That is the mass of a proton. Zero point, and there there are 26 zeros, and then 1673

kilograms. A truly tiny number so how do we deal with this? Well again it's using a similar

trick. If we raise ten to the power of minus one, it means divide by ten, not multiply

by ten. So this means divide by ten which gives you zero point one. Ten to the power

of minus two means divide by ten twice, which gives us zero point zero one, a hundredth.

Ten to the power of minus three means divide by ten three times, or zero point zero zero

one. So again you see a pattern developing. The exponent here tells you how many places

to the right of the decimal that the one is. So in this case, ten to the minus two, the

one is two places to the right of the decimal. Here, ten to the minus three, the one is three

places to the right of the decimal. So in this case I actually have a one that is 27

places to the right of the decimal. So I can write the mass of a proton as 1.673 times

ten to the minus 27 kilograms. And this ten to the minus 27 has the function of putting

this number, 1.673, 27 decimal places to the right of the decimal point. So as a challenge

question to see if you've understood it: if the sun were made entirely of protons, how

many protons would there be in the sun?