# How can I understand “thirty-seconds of a dollar”?

I read the following sentence in the book Options, Futures, and Other Derivatives:

Treasury bond prices in the United States are quoted in dollars and thirty-seconds of a dollar.

Here is my question:

How should I understand the phrase in bold, namely, "thirty-seconds of a dollar"?

I think the plural form "thirty-seconds" means several thirty-seconds of a dollar. Does it make sense?

• You can see bonds prices quoted in 1/32th increments here. As of 2011-10-23 you can see the 5 year note with a 1% coupon quoted with a price of "99-21¾" = 99 + 21.75/32 resulting in a yield of 1.07%. – user786653 Oct 23 '11 at 15:46
• @siyan, were you thinking as follows? By analogy with "thirty-seconds of a minute", or half a minute, "thirty-seconds of a dollar" is 50 cents? That would not be entirely correct. – James Waldby - jwpat7 Oct 23 '11 at 16:40
• I think it ought to be thirty-secondths. – Optimal Cynic Oct 24 '11 at 6:40
• Like .33 is a thirdth and .2 is a fifthth? – Tim Lymington supports Monica Oct 27 '11 at 15:59
• @OptimalCynic Not so. The older usage, from which the modern usage derives, is "the third, fourth, tenth, twelfth, &c part of [a dollar]", consistently employing the ordinal. This generates "first" for numbers greater than 11 ending in the digit "1", "second" for numbers greater than 12 ending in the digit "2", "third" for numbers greater than 13 ending in the digit "3", and "-th" for other numbers, because their ordinals all end in "-th". One thirtieth, one thirty-first, one thirty-second, one thirty-third, one thirty-fourth, and so forth (or 4th). – StoneyB on hiatus Dec 24 '12 at 17:35

• Half a dollar = 50 cents
• A quarter of a dollar = 25 cents
• An eighth of a dollar = 12.5 cents
• A sixteenth of a dollar = 6.25 cents
• A thirty-second of a dollar = 3.125 cents

Stocks used to be traded in fractional parts of a dollar too, but changed to decimal pricing many years ago.

• What does second mean in this – Jan Oct 23 '11 at 13:46
• @Jan: 2 - one half, 4 - one fourth or a quarter, 8 - one eighth, 16 - one sixteenth, 32 - one thirty-second. 'second' is really 'second' and is the ordinal corresponding to 2 as the part of 32, -not- the 'second' in terms of time, a sixtieth of a minute. – Mitch Oct 23 '11 at 14:03
• You can also think "thirty-twoths" if you like - one part in thirty-two. It's incorrect English but it helps get the maths straight. Just remember when you say it you should say thirty-secondths. – Optimal Cynic Oct 24 '11 at 6:43
• Not really many years ago. The NYSE switched from 1⁄16ths to cents in 2001, despite US currency having been decimalized in 1791. – Dan Oct 25 '11 at 0:14

I think the phrase will be easier to understand if you break the sentence into two parts:

• Treasury bond prices in the United States are quoted in dollars.
• Treasury bond prices in the United States are also quoted in thirty-seconds of a dollar.

Now you can view "thirty-second of a dollar" as a new unit for quoting treasury bond prices. The usage of plural form "thirty-seconds" is the same as that of "dollars" in the first sentence above.

The plural is that way because it should be "thirty-second parts of a dollar".

If the unit price were \$0.25, it would be put into words as quarters of a dollar (or quarters, in normal speech). If it were \$0.20, it would be fifths of a dollar. Following this pattern, thirty-seconds of a dollar means "a unit price of \$.03125". It sounds odd because only the US Treasury (as far as I know) uses this particular measurement.

I believe it is a fraction, e.g. 1/32. Though it sounds odd to me, imperial measurements do not always make sense. ;)

• This has nothing to do with imperial measurements, the dollar isn't an imperial measurement. Fractions do not necessarily imply imperial measurements: "half a kilo" is metric. – Hugo Oct 23 '11 at 10:53
• "half a kilo" makes sense. "three and a half thirty-seconds of a pound" makes no sense at all. – TLP Oct 23 '11 at 13:13
• "Making sense" is hardly the standard for determining what system of measurement it belongs to. This is neither imperial nor metric. – jprete Oct 23 '11 at 13:39
• I did not claim it was a unit of the imperial measurement system, such as feet, inches or bushels. I said that it was a fraction, and I made an assumption that it was coming from a culture that uses Imperial measurements, because it makes no sense coming from a metric culture. – TLP Oct 23 '11 at 13:51