The Maths Prof Standard Form part 1

hi I'm the mat Pro and today I'm going to show you how to use standard form standard form is just handy way of writing really big or really small numbers here I've got few examples of really big and really small numbers so I'm going to turn those into standard form and afterwards I'm going to show you how to do it the other way around so let's look at the first few so these are are three large numbers when we turn these numbers into standard form we need to first of all write the number so that it's in between 1 and 10 so in the first example I'm going to write the number three because that number is between 1 and 10 next have to write * 10 now when we're using standard form we always write time 10 it's just the format that we use now we need to write power here because we can't just leave it like this because 3 * 10 is 30 and the number here is 3,000 so we need to look to see how many places we've moved the decimal the decimal used to be here and now if I'm making this number three it's moved to there so you can see the decimal it looks like it's jumped three places here so the power we put on the 10 is three so this is equal to the number 3,000 because 10 cubed is th000 and 3 * 1,000 is 3,000 so here we go we've done the first one that's now in standard form in the next one if we want to write this number between 1 and 10 this number here should be written as 4.2 then remember for standard form you always have to write times 10 so here I'm writing time 10 and then for the power need to check to see how many places the decimal has moved so used to be here and now it's in between the four and the two cuz we've got 4.2 here so when check this time 1 2 3 4 five it's mve five places so the power on the 10 is five okay so this number is now in standard form now the last large number so first thing you need to do is to make sure this number is between 1 and 10 so 5.67 okay so I'm using the same numbers I'm just putting the decimal in between the five and six then as before we write * 10 and then to find the power you check to see how many place the decimal has moved so it used to be there and now we're placing it between the five and the six so if count the digits here I've got seven so that gives me the power on the last question okay now with the small numbers it's almost the same okay it's still the same idea with this number between between one and 10 and timesing by 10 except the power this time is going to be negative so whenever you've got really small numbers like these ones the power on the 10 will be negative power so let's do the first one to make this number between 1 and 10 need to write four then I'm going to write * 10 just as before I'm also going to check to see how many places the decimal has moved and it's moved three times but remember it's negative power because it's small number so this time it's -3 okay the next example same thing as before write the number between 1 and 10 so this becomes 5.6 then we write * 10 and then you count to see how many places the decimal has moved so it used to be here now it's here so it's moved five digits I'm counting 1 2 3 4 5 so the power on this one is -5 now the last one we're going to turn into standard form this time we're going to put the decimal here so that we've got 4.03 because this number is between 1 and 10 then I'm going to write * 10 and then lastly check to see how many places the decimal has moved so we started here now we're there so 1 2 3 4 so starts move four places so the power is -4 so here we've got some examples turning the numbers into standard form now I'm going to show you how to do it the other way around