What determines the precision of a measurement?

Answer 1

The number of significant digits.

For example if you machine a part to 1 millimeter that is 0.001 meters so the significant digits is three. If you only machined the part to 1 centimeter then that would be 0.01 giving your two significant digits.

If you used those parts together then you would only have a total part that is accurate to 1 centimeter so the significant number of digits would be two, the millimeter measurements wouldn't matter.

In engineering you are often given a tolerance; the maximum allowable error. If your tolerance was plus or minus 3 millimeters then you could machine a 5 millimeter part to the size of 8 or 2 millimeters. The significant number of digits would be three since you have a value between 0.002 and 0.008 millimeters. But, once again if you used it with the 0.01 centimeter part then your significant digits would be only two. However, it if was a 10 millimeter part then you are still working in millimeters so the significant number of digits would remain 3.

In the real world your tools and your contract state the tolerance and that determines how precise your measurements are. You can't cut below the millimeter with wood, very easily. In fact wood usually has a tolerance of say 0.1 meters. However, it is easy to cut metal down to the millimeter and a micrometer is a commonly used tool that can measure it. So a tolerance in millimeters is common. But, most shops don't have equipment that can cut down finer than the millimeter so tolerances rarely go any further down than the millimeter level. Which doesn't sound like much until you think that most drive shafts are over 3 feet long so the percentage of error has to be very fine.

In the real world you usually use a tape measure to measure wood. The standard English tape measure has an accuracy down to the 1/16th of an inch. This then becomes the maximum precision that you can cut to. However, depending on the application a error of 1/2” is permissible. Wood has a good deal of wiggle room, but metal doesn't so your tolerances are higher with metal.

Answer 2

The tool you are using to measure.