### Video instructions and help with filling out and completing Are Form 2220 Index

**Instructions and Help about Are Form 2220 Index**

Hi there and welcome to another video from Hegarty maths it's mr. Haggerty here this is video 22 on our GCC higher revision series we're talking about standard form today as always a reminder this video is not supposed to teach you from first principles the understanding of standard form and why it works it's a quick summary of the key facts you need to know for the exam and then a practice of some exam questions as always I'm going to start off by doing some examples just to show you the basic ideas take notes down for that fully concentrate maybe even make a revision card after that there will be several exam questions pause the video when I show it to you try it then play a market of my 100% check you've got it right if you're doing the course online then if it's all right green tick that video if it's a bit wrong couple of mistakes amber you might need to revisit those topics and if it's red you probably need to watch the video again and start over or ask your teacher for help okay firstly standard form very basically what is it well standard form is a way of writing big and small numbers it's a way of writing big or small numbers and it's a way of writing them quickly and efficiently so quickly and efficiently so it always comes up in questions to do with big or small numbers what does a number in standard form look like well it always looks like this it's some number multiplied by a power of 10 10 to some power I'm going to put 10 to the power of n now this number what is must this number be it must be between 1 and 10 it can't be 0.5 because that's below 1 it couldn't be 12 because that's above 10 it's got to be some number between 1 and 10 and what about this this is always a whole number now if it's a positive whole number it talks about big numbers and if it's negative whole number if that was a negative number it would be about small numbers so that's what a number in standard form Wars looks like some number between one and ten multiplied by a power of 10 if that power of 10 if the power is positive we're talking about big numbers if it's negative we're talking about small numbers right let's introduce you to some ideas here firstly let's write a big number like this in standard form what we do as follows the first non-zero digit is the key that's six there so our number between 1 and 10 we're going to take that to be equal to 6 so it's 6 now what power of 10 is it when you count how many digits after that first nonzero 1 2 3 4 5 6 7 8 9 so we're going to say that 6 multiplied by 10 to the power of positive 9 simple as that what about in this case here well again we highlight our first nonzero term which is a 6 we put a lineup trip there are 9 terms after this so our number between 1 and 10 is going to be 6.3 we need to capture the fact that it's not 6 it's 6 point 3 and we're going to multiply it by 10 to the power of 9 now some students say why isn't it 63 times 10 to the power of 8 the reason is this number has to be between 1 and 10 so we write our 6 down then we write 0.3 so and we stop where the zero start then we count how many digits after the first 6 right what about the next one well the key digit is the 5 as always okay now what we have to do is we have to write a number between 1 and 10 that summarizes this I'm going to write 5 point 0 2 we write 5 after the written a 5 right point and we write up to and where the nonzero digits stop now how many nonzero digits after the 5 1 2 3 4 5 6 so it's going to be 5 point 0 2 to the power of 6 now let's go backwards we're given standard form let's convert it into an ordinary number so this was ordinary going to standard form let's go standard form to ordinary so six is our first digit and this seven tells us we've got seven digits after the six and they're all zeros one two three four five six seven only put your commas in at the end every three from the end so three there and three there what about this one we'll be right the six zero three and six is where everything depends on the seven tells us there are seven digits after the six so including these that would be the first the second and now we're going to go third the fourth the fifth the sixth the seventh comma comma there that's how that number would look what about this one will we write down the 5 and the 1 now this power of 5 it tells us there are five digits after the five so including that one it's there's one there two three four five put your commas in all right let's do small numbers well here the non-zero digit is a six and how many digits before the six this time for small numbers one two three four five six seven multiplied by 10 to the power not of seven but negative seven cuz it's small what about this one well again the first nonzero term is six so that's going to be vital but we write six point three to capture the fact that it's not just six on its own and.