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Percent Error Made Easy!

in this video we're gonna focus on

calculating percent error so here's a

problem let's say that you have an

experiment and you're measuring the

density of aluminum let's say you're

measured value is 2.6 grams per cubic

centimeter so this is how much you got

in the experiment now the accepted value

or the actual density of aluminum this

is what you want to get in your

experiment this is the ideal value is

2.7 grams per cubic centimeter so based

on this what is the percent error in

this experiment so here's the former so

the percent error is equal to the

absolute value difference of the

measured value or your experimental

value minus the actual value divided by

the actual value times 100% so the

percent error is going to be the

difference between these two numbers so

we have a measured value of 2.6 and the

actual is 2.7 divided by 2.7 times a

hundred percent so 2.6 minus 2.7 that's

equal to negative point 1 and the

absolute value of negative 0.1 is

positive point 1 so positive point 1

divided by 2 point 7 times 100% let me

get out my calculator let's plug this in

and so I got 3.7% and so this is the

percent error for this experiment now if

you need to calculate simply the error

not epicenter but just the error here's

what you can do the error is the

difference between the measured value

and the actual value so in our example

the measured value was 2.6 grams per

cubic centimeter the actual value is 2.7

so the error is negative point one

because we got a value that is just

under there the actual value and so

that's how you can calculate the error

so now let's try it another problem so

let's say our measured value is seven

point seven grams per cubic centimeter

and this is for the density of iron

metal we're trying to experimentally

measure the density of iron metal and to

measure the density of something density

is basically mass over volume

now the actual density of iron metal is

seven point eight six grams per cubic

centimeter so based on this information

go ahead and calculate the error and the

percent error feel free to pause the

video so let's start with the arrow the

arrow is going to equal the measured

value minus the actual value so the

measured value we saw was seven point

seven and the actual value is seven

point eight six so seven point seven

minus seven point nine six so the error

is negative point sixteen so now to

calculate the percent error

this is equal to the error divided by

the actual value times 100% but this is

the absolute value of the error so

remember the error you can replace it

with the measured value minus the actual

value and if you do it will give you the

first formula that we wrote early in

this video so if I take this and

substitute it for error I'm gonna get

the other version of this formula and

that is the measured value minus the

actual value with an absolute value

symbol divided by the actual value times

100% so let's go ahead and finish it so

I'm going to use the second formula on

the bottom that is this one so percent

error is going to equal the error which

is negative point 16 going to take the

absolute value of that and then divided

by the actual value which is seven point

eight six times a hundred percent so the

absolute value of negative point 16

that's going to be positive point

sixteen so in the calculator type this

in point 16 divided by seven point eight

six times 100 percent and so for the

pecet error i got this answer two point

zero three six percent hopefully you got

the same thing too so that is the

percent error for this experiment so

hopefully this video gave you a good

idea of how to calculate percent error