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In this video we're going to look at how we can use standard form convert numbers into standard form and out of standard form standard form can be a useful way of writing down very large numbers very small numbers so we're going to start with this number and we're going to write it in standard form what you've got to do to write a number in standard form is to look at the number you've got ignore the north's at the end for the time being as long as they're just at the end if there's a naught between the 5 and the 6 I wouldn't ignore that one Ranaut's at the end i could ignore so i've got a 5 and a 6 now I've got to put a decimal point into that number to make it between 1 and 10 so I put my decimal point in there it becomes 5 point 6 I know always write down times by 10 and I write a power up here and that power is how many positions the decimal point has moved from the starting number to the number I've got here now originally the decimal point must have been here at the end it wasn't written in but that's where it must have been so I've moved this decimal point one two three four five times because I put it in between the five and the six so I will put that up there so in standard form this number here which is 560,000 it's five point six times ten to the power of five I do another one three seven oh two oh oh oh oh oh now let's try and work out what that number is it's often useful to come back from the end putting commas in so these are the millions that's three hundred and seventy million two hundred thousand if I'm writing in standard form or ignore noughts at the end and I write down what else I've got which is three seven zero two and I've got to make this number a decimal number between naught and ten so between one and ten so I'll put my decimal point in there three-point 702 the decimal point must have been here to start with even though we didn't bother writing it down so it's moved one two three four five six seven eight times so after my times by 10 which I always write in I'll put a power of eight that's how you do standard form with numbers like that we just do one more will do 56.2 now it's not a particularly big number but it can still be done in standard form remember the first thing you've got to do is write this number down ignoring any notes at the end well there aren't any in this case but you're going to make the number between 1 and 10 by putting a point in so it becomes five point six two then you always put your toes by ten in and here I move the decimal point one place so I put a one up there so that would be the same as five point six two times ten to the power of one sometimes you can have numbers which are very small numbers which are less than one should not point something numbers so here's one naught point naught naught naught for three and what we do here is very similar to what we've been doing so far with one important difference we ignore noughts at the beginning or at the end if there were any there we write this number down so that it's between one and ten so I change it to four point three then I write down my x by ten now I've moved the decimal point one two three four places so I put a four up there but that's not where I finish if you notice this time the arrow has gone the other direction I've gone left to right within the other questions I went right to left to show it's a naught point number to show it went the other way I put a minus in front of that power so let's go through it again if it's a naught point something number you will always have a minus up here so we look at another one nor point naught naught naught - naught 3 I have to change the number to a number between 1 and 10 I ignore notes at the beginning so I'll have to point naught 3 that naught I got to include it's not at the beginning or the end I wrote down my times by 10 and I move that decimal point one two three four places it ended up there I put my 4 in there because a naught point number I put a minus in it's only for naught point numbers you do put those minuses in so let's show you how you get numbers into standard form we also need to see how to get them back out of standard form so if you were given the number three point seven two times ten to the power of five write down your three your seventh and you two now you've got to move this decimal point five times you don't just stick five notes on the end you've got to move the decimal point five times it started there and move it once that will go there move it twice that will go there now I'm going to put notes in move it three times that would go there four times that would go there five times it would go there so that's just the C I've moved that decimal point one two three four five times so that's my answer three seven two zero zero zero or 372,000 the mistake people make is just stick five notes on the end

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