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Hi there and welcome to another video from Hearty math'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 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,...
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