# Is 80% the same as "8 out of 10"? **URL:** \ **Category:** Factual Questions\ **Created:** [April 11, 2005, 11:27pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871 "2005-04-11T23:27:28Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![StarsApart](https://avatars.discourse-cdn.com/v4/letter/s/ecc23a/32.png) [@StarsApart](https://boards.straightdope.com/u/StarsApart)\ **Post date:** [April 11, 2005, 11:27pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/1 "2005-04-11T23:27:28Z")
It seems like a silly question, but I just want to be sure of this. I’m working on a paper for school, and found a resource that uses a statistic involving “8 out of 10” minorities. Can I rephrase this to “80%” in my paper, or would I be better off just quoting it? ---
**Author:** ![sleeepy2](https://avatars.discourse-cdn.com/v4/letter/s/e9a140/32.png) [@sleeepy2](https://boards.straightdope.com/u/sleeepy2)\ **Post date:** [April 11, 2005, 11:28pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/2 "2005-04-11T23:28:45Z")
It’s the same. ---
**Author:** ![StarsApart](https://avatars.discourse-cdn.com/v4/letter/s/ecc23a/32.png) [@StarsApart](https://boards.straightdope.com/u/StarsApart)\ **Post date:** [April 11, 2005, 11:30pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/3 "2005-04-11T23:30:57Z")
Thanks 🙂 ---
**Author:** ![manhattan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/manhattan/32/7_2.png) [@manhattan](https://boards.straightdope.com/u/manhattan)\ **Post date:** [April 11, 2005, 11:33pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/4 "2005-04-11T23:33:34Z")
It’s supposed to be the same, but exercise caution – an uncareful writer might use “8 out of ten” to represent anything from 75% to 84% rounded. If possible, find the source of your source’s statistic. ---
**Author:** ![chaoticbear](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@chaoticbear](https://boards.straightdope.com/u/chaoticbear)\ **Post date:** [April 11, 2005, 11:36pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/5 "2005-04-11T23:36:28Z")
And I was going to say also that 8 out of 10 may also be from a smaller sample size, and therefore not as relevant as a study done with more people, but their MMV ---
**Author:** ![uglybeech](https://avatars.discourse-cdn.com/v4/letter/u/82dd89/32.png) [@uglybeech](https://boards.straightdope.com/u/uglybeech)\ **Post date:** [April 11, 2005, 11:42pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/6 "2005-04-11T23:42:00Z")
It’s not a carelessness issue, it’s a significant figures issue. Your adding the 0 in 80 is adding a significant figure which you shouldn’t do. Not the same. ---
**Author:** ![Diogenes\_the\_Cynic](https://avatars.discourse-cdn.com/v4/letter/d/e99b99/32.png) [@Diogenes\_the\_Cynic](https://boards.straightdope.com/u/Diogenes_the_Cynic)\ **Post date:** [April 11, 2005, 11:48pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/7 "2005-04-11T23:48:21Z")
It depends on how large the sample is. Eight out of ten in a sample of ten is not statistically significant. Eight out of ten in a sample of 2000 is statistically significant. So check to see how large the sample was or how it was chosen. BTW, 80% is a _mathematically_ accurate way to render “8 out of 10,” but it may not be valid to extropolate a general statistic. for the population in question. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [April 12, 2005, 12:55am UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/8 "2005-04-12T00:55:10Z")
> [@uglybeech](#): > > It’s not a carelessness issue, it’s a significant figures issue. Your adding the 0 in 80 is adding a significant figure which you shouldn’t do. Not the same. Since when? 80.0% is three sig figs, but 80% is the only way to write 8/10 in percentage form. ---
**Author:** ![hajario](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hajario/32/171_2.png) [@hajario](https://boards.straightdope.com/u/hajario)\ **Post date:** [April 12, 2005, 1:03am UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/9 "2005-04-12T01:03:25Z")
> [@iamthewalrus(:3=](#): > > Since when? > > 80.0% is three sig figs, but 80% is the only way to write 8/10 in percentage form. 80.0 is three sig figs. 80% is two sig figs. You can also do it with one sig fig: 80 ± 10%. Haj ---
**Author:** ![Antonius\_Block](https://avatars.discourse-cdn.com/v4/letter/a/51bf81/32.png) [@Antonius\_Block](https://boards.straightdope.com/u/Antonius_Block)\ **Post date:** [April 12, 2005, 2:51am UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/10 "2005-04-12T02:51:10Z")
> [@hajario](#): > > 80.0 is three sig figs. 80% is two sig figs. You can also do it with one sig fig: 80 ± 10%. It’s a while since I’ve thought much about sig figs, but shouldn’t that be 80 ± **5%**? ---
**Author:** ![uglybeech](https://avatars.discourse-cdn.com/v4/letter/u/82dd89/32.png) [@uglybeech](https://boards.straightdope.com/u/uglybeech)\ **Post date:** [April 12, 2005, 3:34am UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/11 "2005-04-12T03:34:26Z")
> [@iamthewalrus(:3=](#): > > Since when? > 80.0% is three sig figs, but 80% is the only way to write 8/10 in percentage form. Yup, you’re right, I’m wrong. I entirely retract by [this cite:](http://dbhs.wvusd.k12.ca.us/webdocs/SigFigs/SigFigRules.html) > [@](#): > > 200 is considered to have only ONE significant figure while 25,000 has two. > > This is based on the way each number is written. When whole number are written as above, the zeros, BY DEFINITION, did not require a measurement decision, thus they are not significant. > However, it is entirely possible that 200 really does have two or three significnt figures. If it does, it will be written in a different manner than 200. Sorry for muddling the issue. But I still strongly believe you shouldn’t do it in any formal work. You’ll look like you’re fudging the numbers. ---
**Author:** ![Kozmik](https://avatars.discourse-cdn.com/v4/letter/k/8dc957/32.png) [@Kozmik](https://boards.straightdope.com/u/Kozmik)\ **Post date:** [April 12, 2005, 3:39am UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/12 "2005-04-12T03:39:30Z")
In school, if you have a quiz with 8 questions and the teacher marks two as incorrect then you have 8 out of 10 correct, which means that you got 80% correct. The difference between the quiz and a sample is that the quiz has a fixed quantity. Because a sample is not a fixed quantity, you should refer to “8 out of 10 minorities” So the patient walks into the doctors office and says “I’ve got good news and bad news. The bad news is that 3 out of 10 people with this disease will die. The good news is that I’ve seen 9 patients will this disease already and 3 of them have already died.” See the paradox of statistics. ---
**Author:** ![Fish](https://avatars.discourse-cdn.com/v4/letter/f/bc8723/32.png) [@Fish](https://boards.straightdope.com/u/Fish)\ **Post date:** [April 12, 2005, 9:01am UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/13 "2005-04-12T09:01:07Z")
> [@StarsApart](#): > > I’m working on a paper for school, and found a resource that uses a statistic involving “8 out of 10” minorities. Can I rephrase this to “80%” in my paper, or would I be better off just quoting it? Considering that you are quoting from a source, the honest thing to do is to quote it exactly and give appropriate credit. Further considering that the statistic is “8 of 10 minorities,” I would definitely leave it in that format. I don’t know what your source states, but consider the following: “Students in our school are represented by 10 minority groups, 8 of which are from Asia” means one thing, but “80% of our minority group students are from Asia” is very different statistic indeed. Leave your source exactly as you found it. ---
**Author:** ![Gary\_T](https://avatars.discourse-cdn.com/v4/letter/g/3ec8ea/32.png) [@Gary\_T](https://boards.straightdope.com/u/Gary_T)\ **Post date:** [April 12, 2005, 12:57pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/14 "2005-04-12T12:57:19Z")
The definition of percent is “per 100,” so 80% means “80 out of 100.” As mentioned, this is mathematically the same value as 8 out of 10. As also mentioned, the difference is in significant figures and the possibility of rounding. If 78 out of 100, or 822 out of 1000, were in category X, one might simplify those figures to “8 out of 10” or “80%.” But if one were to be more precise, those figures translate to percentages of 78 and 82, respectively. In your case, you don’t whether or not the “8 out of 10” represents such simplification – the original figures may have reflected anywhere from 76-84%. One way to rephrase “8 out of 10” while acknowledging this possibility is “about 80%.” ---
**Author:** ![mittu](https://avatars.discourse-cdn.com/v4/letter/m/ecd19e/32.png) [@mittu](https://boards.straightdope.com/u/mittu)\ **Post date:** [April 12, 2005, 1:04pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/15 "2005-04-12T13:04:10Z")
Wouldn’t 822 out of 1000 translate to a percentage of 82.2% rather than 80%? ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [April 12, 2005, 1:27pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/16 "2005-04-12T13:27:17Z")
> [@uglybeech](#): > > Yup, you’re right, I’m wrong. I entirely retract by [this cite:](http://dbhs.wvusd.k12.ca.us/webdocs/SigFigs/SigFigRules.html) > Sorry for muddling the issue. But I still strongly believe you shouldn’t do it in any formal work. You’ll look like you’re fudging the numbers. If you measure something and the exact measure is 25,000, then there are five significant figures. If my odometer reads 0 and I drive from Boston to LA and the odometer reads 3000, then the distance is 3000 with 4 significant figures. Sorry to tangenticize. ---
**Author:** ![PatriotX](https://avatars.discourse-cdn.com/v4/letter/p/c4cdca/32.png) [@PatriotX](https://boards.straightdope.com/u/PatriotX)\ **Post date:** [April 12, 2005, 1:51pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/17 "2005-04-12T13:51:56Z")
> [@mittu](#): > > Wouldn’t 822 out of 1000 translate to a percentage of 82.2% rather than 80%? Hence the non-math use of the word “simplify.” > [@CookingWithGas](#): > > If you measure something and the exact measure is 25,000, then there are five significant figures. If my odometer reads 0 and I drive from Boston to LA and the odometer reads 3000, then the distance is 3000 with 4 significant figures. 2500.0 and 3000.0 is what you mean ---
**Author:** ![Bippy\_the\_Beardless](https://avatars.discourse-cdn.com/v4/letter/b/ac8455/32.png) [@Bippy\_the\_Beardless](https://boards.straightdope.com/u/Bippy_the_Beardless)\ **Post date:** [April 12, 2005, 4:16pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/18 "2005-04-12T16:16:23Z")
**uglybeech** you are not wrong. The cite which contradicted you is only really applicable to very precise use within scientific papers and even then is not as I remember being taught 10 years ago doing physics research. 80% could mean 80% ±0.5% or it could mean 80% ±5%. It is ambiguous when 80% is written. To remove the arbitraryness it would need to be written (0.80 x 10[sup]2[/sup]) % for 80% ±0.5%, or (0.8 x 10[sup]2[/sup]) % for 80% ±5%, both of which are too longwinded and complicated for common usage. ---
**Author:** ![Gary\_T](https://avatars.discourse-cdn.com/v4/letter/g/3ec8ea/32.png) [@Gary\_T](https://boards.straightdope.com/u/Gary_T)\ **Post date:** [April 12, 2005, 4:41pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/19 "2005-04-12T16:41:06Z")
> [@mittu](#): > > Wouldn’t 822 out of 1000 translate to a percentage of 82.2% rather than 80%? Yes. But if one were to represent this value as “X out of 10” (X being an integer), X would have to be 8, giving 8 out of 10. If one were then to take “8 out of 10” and express it as a percentage, it would be 80%. The discrepancy between this and the original 82.2% is what I was trying to illustrate. ---
**Author:** ![chaoticbear](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@chaoticbear](https://boards.straightdope.com/u/chaoticbear)\ **Post date:** [April 12, 2005, 4:42pm UTC](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871/20 "2005-04-12T16:42:44Z")
> [@PatriotX](#): > > Hence the non-math use of the word “simplify.” > > 2500.0 > and 3000.0 > is what you mean Well, that would be five significant figures. We don’t have any information about the tenths place on his odometer. [Next page](https://boards.straightdope.com/t/is-80-the-same-as-8-out-of-10/298871.md?page=2)