Scientific Notation - Explained!

Key Takeaways

In science, we often need to deal with some very large numbers. For example, the mass of the sun. That is the mass of the sun. A two followed by 30 zeros in units of kilogram. That is 2,000 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 2 0 0 0. Yes. Sorry. Could you repeat that? I was with you up to 2000 0 uh it was uh 2 0 0. So to represent large numbers easily we use something called scientific notation. Scientific notation takes advantage of powers of 10. For example, 10 the^ of two means take two 10 and multiply them together and you get 100. 10 ^ of 3 means multiply three 10 together and you get a,000. 10 ^ 4 10 the^ 4 means take four 10 multiply them together and you get 10,000. So you should notice a pattern developing. When it's 10 the^ of two, our final answer has a one followed by two zeros. When it's 10 the^ of three, our final answer has a one followed by three zeros. 10 the^ of four again four zeros. So if we wanted to represent the mass of the sun in scientific notation, we would need 30 zeros. So we represent that using 10 ^ of 30. This means we're multiplying 10 by itself 30 times which gives us a 1 followed by 30 zeros. But the mass of the sun is actually twice that. It's 2 followed by 30 zeros. So we can multiply 2 by 10 30 in units of kilogram and that is the mass of the sun. it's a lot easier to write and it takes up much less space on the page. The other problem is we have to deal with some very tiny numbers. For example, the mass of a proton is that is the mass of a proton. 0 and then there's 26 zeros and then 1673 kg a truly tiny number. So how do we deal with this? Well again it's using a similar trick. If we raise 10 to the power of minus1 it means divide by 10 not multiply by 10. So this means divide by 10 which gives you 0.1 10 ^ of minus2 means divide by 10 twice which gives us 0.01 100th 10 ^ of minus 3 means divide by 10 three times or 0.001. So again you see a pattern developing. The exponent here tells you the number of places to the right of the decimal that the one is. So in this case 10 the minus2 the one is two places to the right of the decimal. Here 10us 3 the one is three places to the right of the decimal. So in this case I have a one that is actually 27 places to the right of the decimal. So I can write the mass of a proton as 1.673 times 10us 27 kg. And this 10us 27 has the function of putting this number 1.673 uh 27 decimal places uh 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?