[Music] in this video we're looking at standard form which is just a special way of writing numbers particularly those that are really big or really small the key point to remember is that we always have to write standard form in this general format where a which we can call the front number is a number bigger than or equal to 1 but less than 10 while n which we call the power or the index can be any positive or negative whole number to see what i mean let's take a look at these four numbers and see if each of them are in standard form or not the first one 4.5 times 10 to the power of 4 is correct standard form because the front number 4.5 is between 1 and 10 and the power or index of 4 is a whole number this second one 0.7 times 10 to the power of minus 2 though isn't in standard form because 0.7 which is the front number is less than 1. 9.34 times 10 to the power of 5.5 also isn't correct standard form the front number of 9.34 is fine because it's between 1 and 10 but the power isn't a whole number so it doesn't count as standard form the last number 1 times 10 to the power of minus 13 is absolutely fine the front number is okay because it's allowed to be one itself and the index is fine because negative 13 is a whole number now the way that standard form works is that if the power is positive then it tells us how many times we need to multiply the front number by 10. for example 2.7 times 10 to the power of positive 3 means 2.7 multiplied by 10 three times so we can see that its actual value is two thousand seven hundred meanwhile if the index is negative it tells us how many times we have to divide our front number by ten so 5 times 10 to the power of negative 2 is just 5 divided by 10 twice so 0.05 and so if you think about it this means that anything with a positive index is going to be a relatively big number whereas anything with a negative index is going to be a fairly small number now another way that you can think about these powers is that they tell us the number of places that we need to move the decimal point if the power is positive then you move the decimal point to the right making the front number bigger but if the power is negative then you move the decimal point to the left making the front number smaller so for 2.7 times 10 to the power of positive 3 the positive 3 tells you that you're going to have to move the decimal point 3 places to the right to do this we write out the 2.7 and then using little arrows move the decimal point three places to the right so one two three which means that our new decimal point would be here then you just fill in all the empty spaces with zeros and remove the old decimal points so we end up with 2 700 and because there aren't any decimal places we actually don't need the decimal point anymore for five times ten to the power of negative two the negative two part means that you need to move the decimal point two places to the left this time so you write out the five but also need to add a point zero so that you can work with the decimal point next you can add your arrows going two places to the left so one and two and then add the new decimal point and the zeros into the gaps and to finish we can just remove the old decimal point and if we want we can also get rid of this zero that we don't really need anymore leaving us with 0.05 as our answer anyway that's everything for this video so hope it all made sense and we'll see you again soon