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Scientists (and engineers) are used to taking measurements and working with numerical data. With numerical data, we can try to identify patterns hidden in nature. With those patterns, we can begin to understand, predict, and perhaps ultimately control the world that surrounds us. Because data is so important to scientists and engineers, sometimes they need to worry about more than just whether they are right or wrong. They have developed what seems like a secret language to help them describe their measurements in more detail.

What is the difference between a Number and a Measurement?
Measured numbers or ‘measurements’ are fundamentally different from numbers. A measurement is a combination of a number and a unit. The number tells you how much (or how little) of something you have. The unit tells you what you actually have measured. Watch Crash Course Chemistry and learn more about why units are so essential! Combining a number and a unit together, we get a measurement. For example, “6” is not a measurement, but “6 meters” is.

Taking a measurement requires you to use a measuring tool of some sort: a ruler, a thermometer, a graduated cylinder, etc. Check out this Bill Nye the Science Guy Episode on measurement! When you measure, you must interpret the measurement against the standard established by the tool. In the process, you put a little bit of yourself into the measurement and, for this reason, the tool you use to measure has a big impact on the result you get. The existence of a measurement, not surprisingly, means that someone actually measured it. There is a natural limit to how well I can measure objects depending on how well I can ‘see’ it as well as how good of a tool I am using to see it.

What is accuracy? What is precision?
Ever wonder about the difference between accuracy and precision? Accuracy is the easy one. Ask the question, “Is my answer in agreement with the right answer?” What is the temperature outside right now? How many calories did I eat today? Was the fish that Uncle Frank caught really 27 inches long?

What can change the accuracy of a measurement? Sometimes, we simply don’t know how to use the tool properly. A classic example of this is using a measuring tape that has inches on one side and centimeters on the other. The measuring tape starts off on the inches side, but accidentally flips over during use and ends up on the centimeter side. If you aren’t careful, you might read the final result as inches, when really you’re measuring centimeters. That will definitely be an inaccurate result.

While accuracy is easy enough to understand, it does have an underlying weakness. I could tell you that my record is eating 47 ounces of jellybeans in one sitting, but who is to say if I’m telling the truth or not. As fellow scientists (and engineers), we can only assume that the person taking the reading did the best they could, unless their research gives us reason to think otherwise.

Be careful though, some people assume that if you write a lot of digits after the decimal point, the measurement has to be accurate. Sometimes a large number with lots of decimals sounds much more authoritative but is no guarantee of being correct. After all, I could have misread the display or forgot to calibrate the scale.

What is precision? There is a protocol that scientists and engineers follow when faced with this situation. The only way that you can be more certain (or precise) when measuring is for you to switch to a better tool. When I say ‘better’, I mean ‘more finely incremented’. When your instrument is more finely divided, that normally gives you the confidence to state a measurement to more digits, or a higher PRECISION.

Several people who look at the same situation might choose widely different measurements to represent their interpretation of it. They may all cluster around the right answer, but they will fall above or below it to a certain amount based on the precision of the tool available. On the other hand, a more finely divided tool creates the opportunity for ‘exactness’ of a measurement.

The Golden Ruler of Measurement says you can only be as precise as BOTH your tool and your circumstances allow. Once you enter the realm where you can’t say FOR SURE what the number is, you’ve hit your estimated digit and should end it there. That could mean, under certain circumstances, that you don’t use the full ‘precision potential’ of your measuring tool.

Significant Digits (or Figures)
What are significant digits? If you read a measurement from someone who understands the Golden Ruler, then you have access to some secret information about the circumstances under which the measurement was taken. 

It is pretty cool that you can infer the tool he used from just the measurement! And THAT is what makes significant digits (or figures)… well, SIGNIFICANT. Check out this video from Khan Academy for more understanding.