this lecture is about how to do calculations with significant figures I'll go over how to correctly record significant figures in your answer when you're performing addition and subtraction multiplication and division and I'll also go over powers and roots when you're adding or subtracting numbers you have to always round the answer to the same number of decimal places as the value with its rightmost significant figure in the greatest decimal place so I'll give you a few examples of what that means in problem number one I have 4.0 three plus five point four if I look at the rightmost significant figure of both numbers in the first number it's in the hundredths place and in the second number is in the tenths place the tenths place is greater than the hundredths place so I'm going to have to round my answer to the tenths place so when I add these together I get nine point four three and rounding to the tenths place gets me nine point four so that would be the correct way of recording that result and respecting the significant figures in problem - I have 510 - 418 and you'll remember that because we don't have a decimal that's 0 and 510 doesn't count as significant so because that's bigger than the ones place where the 8 is at that will be the place where I round to when I do the subtraction so I subtract and then I round to the tens place which gives me 90 in problem 3 I do have a decimal point in both numbers so the zeros and 4300 are significant so I'm going after round to the ones place and my answer which gets me 4 4 1 8 in problem for the first number goes down to the thousandths place and the second number goes down to the hundredths place so I need to round to the hundredths place so we need your answer this which gets me point oh six problem five is written in scientific notation so I'm just going to rewrite that just so I can see a little bit more clearly which decimal place each number goes to I can see that the left number goes to the tens place and the right number goes to the hundreds place so I'll round to the hundredths place problem six is also in scientific notation and if I want to rewrite that in scientific notation this is how it would look in problem 6 I'm subtracting two numbers in scientific notation and I'll rewrite them so it's a little more clear so I can see that first number is in the hundreds spot and the second phone and the second number is a hundreds spot so I'll round to the hundreds spot so that would be my answer moving on to multiplication and division the rule works a little differently when you're multiplying or dividing two numbers with significant figures you have to round the answer to the same number of significant figures as the value in the problem with the least number of significant figures so I no longer care about the decimal place I only care about the number of significant figures and I'll always round to the least number in problem number one the first number has three sig figs and the second number only has one so we need to round my answer to only have one significant feed because that's the lower number of sig figs so when I round that that comes out to be 60 problem two is division and I have four sig figs in my numerator and because that decimal point is there in the 30 I have two sig figs in my denominator so I have to round the answer to two significant figures so that would be the answer in problem three I have a number with two sig figs and a problem with three sig figs because again that decimal point is there so that means I have to round this number to two significant figures so this could be four four zero with a decimal point after but the problem is that that decimal point is making that zero significant so we actually have to remove that decimal point so that the zero is no longer significant and I only have two significant figures in problem number four I have two sig figs over three sig figs so I round to two in problem number five I have three sig figs times five sig figs so I'll round to three significant figures finally in problem six we're doing a division where we have four significant figures over four significant figures so my answer will also have four significant figures so this will be my answer reading that to four sig figs gets me zero point eight nine seven eight so that's how you do multiplication and division while respecting significant figures finally we can go on to powers and roots the rule here is to round the answer to the same number of significant figures as the number being raised to the power or group so we'll go through the examples in example one I have a number with three significant figures being raised to the fourth so I raise it to the fourth power and then round it to three significant figures and this is what again in problem number two I have a number with two significant figures and we're taking the square root so I know that the square root of 16 is 4 but my answer has to have 2 significant figures in it so to add more significant figures I'm going to rewrite this number as 4.0 that would be the correct way of writing it so that it still has the same number of significant figures as the original number in problem 3 this problem has three significant figures so raising that so the third gets me this and I'll round it to three significant figures and this is my answer in problem number four this number only has one significant figure so when I take the square root I have to round this to just one significant figure as well number five we have four significant figures surrounding that gets me this answer and in problem six I have two significant figures so taking the cubic root gets me to point one times 10 squared so that's how you do calculations while respecting significant figures