Answer:
1. 11 3/4
2. 29 7/16
3. 21 3/8
Step-by-step explanation:
The numbers against the longest marks are the integer portion of the measurement. Tapes that measure inches are marked this way, so we'll presume these are inch measurements. (There is nothing in your picture indicating the unit of measure.)
Each interval between two inch marks is divided into 16 equal parts. The marks get progressively shorter for 1/2, 1/4, 1/8, and 1/16 units. As you would expect, the mark halfway between the numbers is at 1/2 unit, or 1/2 inch more than the smaller of the two integers. The next shorter mark midway in the space between the 1/2 mark and the integers marks 1/4 unit. As you know 1/2 of 1/2 is 1/4. The second-shortest mark is at intervals of 1/8 either side of the 1/4 and 1/2 marks.
Equivalent fractions for numbers of 16ths also give you a clue as to how to read this.
integer inches . . . longest mark
1/16 = 1/16 . . . shortest mark
2/16 = 1/8 . . . second shortest mark
3/16 = 3/16
4/16 = 1/4 . . . third shortest/longest mark
5/16 = 5/16
6/16 = 3/8 . . .second shortest mark
7/16 = 7/16
8/16 = 1/2 . . . second longest mark
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1. The middle mark between 11 1/2 and 12 is 11 3/4, so that is the measure indicated here.
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2. The smallest mark is 1/16 less than 1/2, so is 7/16 more than 29. The measure shown is 29 7/16.
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3. The second smallest mark is 2/16=1/8. This amount less than 21 1/2 (or more than 21 1/4) is 21 3/8.
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While it is common for inch rulers to be divided into 16ths, some specialty rulers have other divisions. Engineering rulers may be divided into 10ths, 20ths, 30ths, 40ths, 50ths, and 60ths (6 scales). Architectural rulers are divided in such a way as to make certain scale factors easy to read. It is not uncommon for the first inch or two to be divided into much smaller divisions, 100ths or 64ths or 32nds, for example.
