I usually hear plural come next: One and a half teaspoons of sugar, one-and-a-half pages of data, e.g.
Also, you can switch to a singular noun if you reword the phrase:
- The play went on for another one-and-a-half hours
- The play when on for another hour and a half
I found this usage note in Macmillan:
When half forms part of a number, the most common structure is one and a half, two and a half, three and a half, etc.
✗ Tourists can visit any of these sites within one and half hours.
✓ Tourists can visit any of these sites within one and a half hours.
✗ They made us wait for two hours and a half for our visa.
✓ They made us wait two and a half hours for our visa.
Always use a plural noun in this structure:
✗ A 90-minute movie might last two and a half hour with commercials.
✓ A 90-minute movie might last two and a half hours with commercials.
The last example shows two and a half, but the wording would be the same for one and a half:
✓ A 60-minute movie might last one and a half hours with commercials.
Incidentally, you can find many forums about this very issue simply by Googling "one and a half hours". Evidently, you're not the first person to wonder about this.
Moreover, some sources recommend using hyphens:
When used as compound adjectives, expressions like four-and-a-quarter and two-and-a-half should be hyphenated to aid your reader and to eliminate ambiguity.
- Expressions like three-and-a-half (as in three-and-a-half ounces) are classified as compound adjectives and should be hyphenated. This is done to group the words together to show they are all part of the same adjective.
But this is a style issue, not a prescriptive one.
Here's where it might get tricky: when preceded by an article, and used as a compound adjective, you use a singular unit, not a plural one. Notice how the wording changes in this dialog:
We played a two-and-a-half hour game.
Really, was it that long?
Yes, it lasted two and a half hours.