Which would be 33% the original price.
For the opposite word, "expensive", it all depends on the word before it: "as expensive" or "more expensive".
"100 widgets cost $100. Unit price is $1." They are now twice _as_ expensive -> they now cost $200. Unit price is now $2.
"100 widgets cost $100. Unit price is $1." They are now two times _more_ expensive -> they now cost $300. Unit price is now $3.
But How do you do this with the word "cheap"? Does "cheaper" clearly mean "3x as cheap" or "3x more cheap" (which even sounds a bit wrong)? I guess it means "more cheap" means "cheaper".
Better to avoid the problem and say "They are now two times the cost, or half the cost". Which is much clearer.
Frustratingly, I find this isn't always true in practice. Lots of people use "x times as y" and "x times more y" interchangeably. To avoid ambiguity I try to only use the former in any context where precision is useful.
It’s also used more generally for buy one get one X% off sales and you’ll see lots of “BOGO50” promo/coupon codes. Then marketing jumped on the bandwagon and started plastering “BOGO” all over marketing material so consumers are used to the lingo now
Let's say you have a product for sale at $32. Then you have a sale to boost name recognition, and have a coupon for $32 dollars off (limited time offer). Or equivalently, that would be $32 cheaper. So the net price is free ($0). $32 cheaper = 100% cheaper = 1x cheaper. Likewise, 25% cheaper = 25% less expensive, or doing the math $32 - 0.25*$32 = 0.75*$32 = $24.
"cheaper" isn't a defined operation except for "a is cheaper than b".
So the statements "6% cheaper" and "2 times cheaper" are shorts for "it is cheaper, it costs 6% less" and "it is cheaper, you get 2 times more for the same amount of money".
The parent you're replying to seems to have things confused. 100% off isn't 1x cheaper -- it's infinitely cheaper.
No, it isn't sensible, and is certainly confusing, and that is why you should commit to never using that phrasing from this day forward. It isn't like there is a hardship you have to overcome when using precise language. There are plenty of alternative ways to state the desired objective that are clear and unambiguous:
- The product is now half-priced!
- The item costs half as much!
- The unit comes with a 50% discount!In the headline of this page, it wouldn't have taken but a moment to write a phrasing that would be understandable to all readers of the page. It could read, "GPT-3 will be Two Thirds Less," or, "GPT-3 will cost One Third the Price."
This example from a non-native English speaker shows the difficulties of having several possible interpretations, at least three! [1]
[1] https://forum.wordreference.com/threads/%C2%ABx-times-less%C...
> We’re making our API more affordable on September 1, thanks to progress in making our models run more efficiently.
If you visit the page the price change is pretty clear, they show the before and after. 1k tokens will be anywhere from 1/2 to 1/3 the current price depending on which model you're using.
I think this is more intuitive for most people than using percent difference for the same reason using a raw ratio (speed up) is better for expressing performance improvement.
That (usually) makes no sense, so I assume people mean something else when they say it, but I never have any clue what. Is it a third of the original price? Is it two thirds (new_price = price - price/3)?
Percentages also work this way. If I say "10% cheaper", most people understand that I mean the price is 90% of what it was previously. Although percentages get weird when increasing the price.
e.g. if it was a flat doubling, I would say that as "200% of the price" (new_price = price*(200/100)).
However, I take "200% more expensive" to mean new_price = price + price*(200/100). To me, the "more" implies addition specifically.
"Its cheaper, you get 3 times as much for the same price"
"Its cheaper, it costs 66% less"
Most people aren't well versed in math and just says something that kinda makes sense to them based on the numbers they know.
Assuming that if, say, the service was 25% cheaper than the nominal price last month, it is now 0.25 * 3 = 75% cheaper than the nominal price. However, it would make more sense to advertise that as a 75% discount over nominal price, so probably that's NOT what they meant.
That's the only explanation that makes sense arithmetically, I believe. There cannot be another interpretation of "3x cheaper" unless you reinterpret the word "cheaper."
An order of magnitude is an exponential change of plus or minus 1 in the
value of a quantity or unit. The term is generally used in conjunction with
power-of-10 scientific notation.
Order of magnitude is used to make the size of numbers and measurements of
things more intuitive and understandable. It is generally used to provide
approximate comparisons between two numbers. For example, if the
circumference of the Sun is compared with the circumference of the Earth,
the Sun's circumference would be described as many orders of magnitude
larger than the Earth's. [1]
An order of magnitude is an approximation of the logarithm of a value relative to some
contextually understood reference value, usually 10, interpreted as the base of the
logarithm and the representative of values of magnitude one. [2]
For this item to become 3x cheaper would mean for its cheapness score to be multiplied by 3, thus 1/10 antidollars. Thus “3x cheaper” means the same thing as “price multipled by one third”.
A 33% discount would be "1.5x cheaper" by my analysis.