in this video we're going to look at how to round numbers to a certain number of significant figures to begin though let's quickly recap what significant figures are using these two numbers as examples the first significant figure of a number is the first non-zero digit as you read the number from left to right so in 3 3476 the three is the first significant figure because that's the first digit reading from left to right and importantly it's not a zero whereas for 0.004031 it is 4 is the first significant figure because as we read from left to right these first three digits are all zeros so we don't count them once you've found the first significant figure every digit after it is another significant figure so for and seventy 3476 this four would be the second significant figure the seven would be the third and the six would be the fourth meanwhile for 0.0040 this zero would be the second significant figure the three would be the third and the one would be the fourth and notice that this time the zero does count as a significant figure because it's to the right of the first significant figure so with that out of the way let's now try a couple of questions to round 3476 to two significant figures the first thing we do is find the second significant figure which is this for we can call this the last digit and this is the number that we have to round up or down to figure out if we round up or down though we have to look at the next digit so the seven which we call the decider because it decides which way we round if the decider is 4 or less then we keep the last digit the same but if it's 5 or more we have to round up the last digit so because the decider here is seven we have to round this four up to a five and now because we rounded it we change these last two digits to zeros and finish by writing in the three in front giving us 3500 as our answer another way of thinking about it is that because our last digit was in the hundreds column we just round the whole number to the nearest hundred so three thousand four hundred and seventy six becomes three thousand five hundred for this next one we need to round zero point zero four to three significant figures so this time the first thing we do is find the third significant figure which is this three and we can label this our last digit next we look at the number on the right which is our decider and because it's a 1 which counts as being 4 or less it tells us we're going to have to keep the last digit the same so we keep our last digit as a three and the decider becomes a zero however whenever we round decimals like this we actually don't keep any zeros at the end of the number so we'd get rid of it and end up with 0.00403 now one last thing i want to mention is that one annoying thing with significant figures is that with the number like 4300 we can't really tell whether it has two significant figures or four this is because it could have been rounded to two significant figures from a number like 4315 or something but it could also be exactly 4 300 and not have been rounded at all in which case the two zeros would count as significant figures as well there isn't really any way of knowing which one it is and it shouldn't really matter in your exams but it is worth you being aware of anyway that's everything for this video so hope you found it useful and we'll see you again soon you