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One of the most useful tools in a tradesman's toolbox is the common tape measure. Let's see how to read a tape measure.
The tape measure can be marked with English measurements, metric measurements or both shared on the same tape. Most tape measures have common elements to be able to use them easily. Most tape measures have both inches and foot marks. Notice that the 16", 32", 48", 64", etc. are marked differently than the other inch markers. Some tape measures have small black diamonds with a box around the number, other tape measures have these numbers highlighted in red. These numbers refer to the 16" centers for laying out studs and joists. Most carpenters have the 16" centers memorized up to 8', but a little help on the tape measure is well received when you get to 128".
When you read a tape measure a little knowledge of math is needed. We know that 1/2 is the same as 4/8, 8/16, 16/32, etc. We could refer to the 1/2" mark as the 16/32" mark but we usually use the simplest numbers possible. Since we know that 16/32 is 1/2, when looking for 15/32" on the tape measure, for example, it is the first 32nd before the 1/2" mark.
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Actually, in the field a carpenter refers to a 32nd as plus or minus a major fraction. For instance, 13/32 is 1/32 less than 14/32 or 7/16, so we say "7/16 minus" and 11/32 is 1/32 more than 10/32 or 5/16, so we say "5/16 plus". This is a fast way of reading the tape measure on the job when taking a measurement of something to cut it to fit. What you should do is memorize the common fractions down to sixteenths.
Here they are:
1/16, 1/8, 3/16, 1/4, 5/16, 3/8, 7/16, 1/2, 9/16, 5/8, 11/16, 3/4, 13/16, 7/8, 15/16 and the inch mark.
Notice the size of the graduations on the tape measure changes with the fraction; 1/2 is the largest, then 1/4 and 3/4, then the eighths, sixteenths and the smallest are the thirty-seconds. These divisions are the most common, but you can get a tape measure in tenths and hundredths. I have a framing square that divides an inch into one hundredths.
We use thirty-seconds in the stair calculator, and other instances like that, just for accuracy because when you're cutting 16 stair risers, if you are 1/16th inch out on each stair, you are out a whole inch at the end. Even being 1/32" out gives an error of 1/2"!
Dave
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