In the real world, you’re measuring with significant figures.
You draw a 1 cm line with a ruler. But it’s not really 1 cm. It’s 0.9998 cm, or 1.0001, or whatever. The accuracy will get better if you have a better ruler: if it goes down to mm you’ll be more accurate than if you only measure in cm, and even better if you have a nm ruler and magnification to see where the lines are.
When you go to measure the hypotenuse, the math answer for a unit 1 side triangle is 1.414213562373095… . However, your ruler can’t measure that far. It might measure 1.4 cm, or 1.41, or maybe even 1.414, but you’d need a ruler with infinite resolution to get the math answer.
Let’s say your ruler can measure millimeters. You’d measure your sides as 1.00 cm, 1.00 cm, and 1.41 cm (the last digit is the visual estimate beyond the mm scoring.) Because that’s the best your ruler can measure in the real world.
And this comes up in some fields like surveying. The tools are relatively precise, but not enough to be completely accurate in closing a loop of measurements. Because of the known error, there is a hierarchy of things to measure from as continual measurements can lead to small errors becoming large.
In the real world, you’re measuring with significant figures.
You draw a 1 cm line with a ruler. But it’s not really 1 cm. It’s 0.9998 cm, or 1.0001, or whatever. The accuracy will get better if you have a better ruler: if it goes down to mm you’ll be more accurate than if you only measure in cm, and even better if you have a nm ruler and magnification to see where the lines are.
When you go to measure the hypotenuse, the math answer for a unit 1 side triangle is 1.414213562373095… . However, your ruler can’t measure that far. It might measure 1.4 cm, or 1.41, or maybe even 1.414, but you’d need a ruler with infinite resolution to get the math answer.
Let’s say your ruler can measure millimeters. You’d measure your sides as 1.00 cm, 1.00 cm, and 1.41 cm (the last digit is the visual estimate beyond the mm scoring.) Because that’s the best your ruler can measure in the real world.
Millimeters are 1/1000 of a meter, or 1/10 of a centimeter (which is 1/100 of a meter).
Whoops, fixed.
It’s not fixed. Millimeters aren’t 1/100 of a centimeter.
It is fixed. Your ruler shows 1.0, and then you estimate 1 digit past to 1.00 +/- 0.01.
You’re not making any estimation within 1/10 like that. 1/2 is as close as you can reasonably get.
Ok, well I didn’t come up with the system so please write to the heads of science to get it changed.
You jest, but this seriously is not standard practice in academia or professionally.
And this comes up in some fields like surveying. The tools are relatively precise, but not enough to be completely accurate in closing a loop of measurements. Because of the known error, there is a hierarchy of things to measure from as continual measurements can lead to small errors becoming large.
I used to think that “1 + 1 = 3 for high enough values of 1” was a joke until I realised it’s actually true when it comes to real-world measurements.