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Is the percentage symbol a constant?

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5

$begingroup$

Isn't the percentage symbol actually just a constant with the value $0.01$? As in
$$
15% = 15 times % = 15 times 0.01 = 0.15
$$
I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?

percentages unit-of-measure

share|cite|improve this question

edited 2 hours ago

Vinyl_coat_jawa

2,5441029

asked 2 hours ago

Rudolph GottesheimRudolph Gottesheim

1263

New contributor

Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Right, you can very well see $%$ as a numerical constant, though culturally this would shock many people.
  $endgroup$
  – Yves Daoust
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is not a unit of measure; it is only a useful symbol. 15% is $dfrac {15}{100}$. A percentage is a number.
  $endgroup$
  – Mauro ALLEGRANZA
  2 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I agree completely that % can be considered a real number.
  $endgroup$
  – JP McCarthy
  2 hours ago
  

  
  
  
  

add a comment | 

5

$begingroup$

Isn't the percentage symbol actually just a constant with the value $0.01$? As in
$$
15% = 15 times % = 15 times 0.01 = 0.15
$$
I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?

percentages unit-of-measure

share|cite|improve this question

edited 2 hours ago

Vinyl_coat_jawa

2,5441029

asked 2 hours ago

Rudolph GottesheimRudolph Gottesheim

1263

New contributor

Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Right, you can very well see $%$ as a numerical constant, though culturally this would shock many people.
  $endgroup$
  – Yves Daoust
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is not a unit of measure; it is only a useful symbol. 15% is $dfrac {15}{100}$. A percentage is a number.
  $endgroup$
  – Mauro ALLEGRANZA
  2 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I agree completely that % can be considered a real number.
  $endgroup$
  – JP McCarthy
  2 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Isn't the percentage symbol actually just a constant with the value $0.01$? As in
$$
15% = 15 times % = 15 times 0.01 = 0.15
$$
I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?

percentages unit-of-measure

share|cite|improve this question

edited 2 hours ago

Vinyl_coat_jawa

2,5441029

asked 2 hours ago

Rudolph GottesheimRudolph Gottesheim

1263

New contributor

Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited 2 hours ago

Vinyl_coat_jawa

2,5441029

asked 2 hours ago

Rudolph GottesheimRudolph Gottesheim

1263

New contributor

Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited 2 hours ago

Vinyl_coat_jawa

2,5441029

asked 2 hours ago

Rudolph GottesheimRudolph Gottesheim

1263

New contributor

Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited 2 hours ago

Vinyl_coat_jawa

2,5441029

edited 2 hours ago

Vinyl_coat_jawa

2,5441029

asked 2 hours ago

Rudolph GottesheimRudolph Gottesheim

1263

New contributor

Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 hours ago

Rudolph GottesheimRudolph Gottesheim

1263

7 Answers
7

active

oldest

votes

4

$begingroup$

Yes, for calculations you can use $%=frac{1}{100}$. Of course what is meant by the symbol is an interpretation as "parts of hundred", i.e. as percentage of a given amount.

share|cite|improve this answer

answered 2 hours ago

JamesJames

1,622217

$endgroup$

add a comment | 

2

$begingroup$

I would´t say that $%$ has a value. You can think of $%$ as "multiply by $frac{1}{100}"$. As a sort of a postfix. In the same way as you can think of the "kilo-" prefix as "multiply by $1000$".

So $5%$ meaning
$$
5 text{multiply by} frac{1}{100}=frac{5}{100}=0,05
$$
in the same way as
$$
2 text{kilograms}=2 (text{multiply by $1000$}) grams= 2000 text{grams}
$$

I usually teach my students this way and I found it to work just fine.

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Vinyl_coat_jawaVinyl_coat_jawa

2,5441029

$endgroup$

add a comment | 

0

$begingroup$

Well, it really depends. In Chinese schools, students are told that $100%=1,40%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.

However, it is agreed around the world that you should not write something like "$250%$ liters of water".

So it is a good idea to think of it as a constant, but not write it as a constant.

Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Holding ArthurHolding Arthur

982317

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
  $endgroup$
  – Yves Daoust
  1 hour ago
  
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I believe you can think of it both ways.

It’s a symbol for “parts of a hundred” that happens to have a constant value behind it, and at the same time it’s a constant that happens to have a symbolic meaning behind it.

share|cite|improve this answer

answered 1 hour ago

Victor S.Victor S.

31119

$endgroup$

add a comment | 

0

$begingroup$

I don't think it has a universally agreed nature.(Symbol,constant,or Unit, or else?) Even though it might have had a single nature at the moment it was created, after a long time usage by people, with non-mathematicans as the majority, its nature might be different among different people's point of view.

In my opinion, I would regard '%' equivalent to the phrase 'out of 100'. That means 15% is read as '15 out of 100' . However, I am pretty sure someone else will have his own interpretation on '%' which leads no contradiction to mine.

share|cite|improve this answer

answered 1 hour ago

Anson NGAnson NG

20819

$endgroup$

add a comment | 

0

$begingroup$

The percent sign is an abbreviation: just substitute "$color{red}%$" by "${}color{red}{cdotfrac{1}{100}}$", that's all. So for example: $15color{red}{%}=15color{red}{cdotfrac{1}{100}}=0.15$. Or the other way round: $1.23=123color{red}{cdotfrac{1}{100}}=123color{red}{%}$.

share|cite|improve this answer

answered 1 hour ago

Michael HoppeMichael Hoppe

11.1k31836

$endgroup$

add a comment | 

0

$begingroup$

No, take for example $20 + 50%$. This is equal to $30$, while $20 + 50 cdot 0.01 = 20.5$

share|cite|improve this answer

answered 15 mins ago

PaulPaul

1,642910

$endgroup$

add a comment | 

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4

$begingroup$

Yes, for calculations you can use $%=frac{1}{100}$. Of course what is meant by the symbol is an interpretation as "parts of hundred", i.e. as percentage of a given amount.

share|cite|improve this answer

answered 2 hours ago

JamesJames

1,622217

$endgroup$

add a comment | 

4

$begingroup$

Yes, for calculations you can use $%=frac{1}{100}$. Of course what is meant by the symbol is an interpretation as "parts of hundred", i.e. as percentage of a given amount.

share|cite|improve this answer

answered 2 hours ago

JamesJames

1,622217

$endgroup$

add a comment | 

$begingroup$

Yes, for calculations you can use $%=frac{1}{100}$. Of course what is meant by the symbol is an interpretation as "parts of hundred", i.e. as percentage of a given amount.

share|cite|improve this answer

answered 2 hours ago

JamesJames

1,622217

$endgroup$

share|cite|improve this answer

answered 2 hours ago

JamesJames

1,622217

answered 2 hours ago

JamesJames

1,622217

answered 2 hours ago

JamesJames

1,622217

2

$begingroup$

I would´t say that $%$ has a value. You can think of $%$ as "multiply by $frac{1}{100}"$. As a sort of a postfix. In the same way as you can think of the "kilo-" prefix as "multiply by $1000$".

So $5%$ meaning
$$
5 text{multiply by} frac{1}{100}=frac{5}{100}=0,05
$$
in the same way as
$$
2 text{kilograms}=2 (text{multiply by $1000$}) grams= 2000 text{grams}
$$

I usually teach my students this way and I found it to work just fine.

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Vinyl_coat_jawaVinyl_coat_jawa

2,5441029

$endgroup$

add a comment | 

2

$begingroup$

I would´t say that $%$ has a value. You can think of $%$ as "multiply by $frac{1}{100}"$. As a sort of a postfix. In the same way as you can think of the "kilo-" prefix as "multiply by $1000$".

So $5%$ meaning
$$
5 text{multiply by} frac{1}{100}=frac{5}{100}=0,05
$$
in the same way as
$$
2 text{kilograms}=2 (text{multiply by $1000$}) grams= 2000 text{grams}
$$

I usually teach my students this way and I found it to work just fine.

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Vinyl_coat_jawaVinyl_coat_jawa

2,5441029

$endgroup$

add a comment | 

$begingroup$

I would´t say that $%$ has a value. You can think of $%$ as "multiply by $frac{1}{100}"$. As a sort of a postfix. In the same way as you can think of the "kilo-" prefix as "multiply by $1000$".

So $5%$ meaning
$$
5 text{multiply by} frac{1}{100}=frac{5}{100}=0,05
$$
in the same way as
$$
2 text{kilograms}=2 (text{multiply by $1000$}) grams= 2000 text{grams}
$$

I usually teach my students this way and I found it to work just fine.

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Vinyl_coat_jawaVinyl_coat_jawa

2,5441029

$endgroup$

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Vinyl_coat_jawaVinyl_coat_jawa

2,5441029

edited 1 hour ago

J. W. Tanner

2,3611117

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Vinyl_coat_jawaVinyl_coat_jawa

2,5441029

answered 1 hour ago

Vinyl_coat_jawaVinyl_coat_jawa

2,5441029

0

$begingroup$

Well, it really depends. In Chinese schools, students are told that $100%=1,40%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.

However, it is agreed around the world that you should not write something like "$250%$ liters of water".

So it is a good idea to think of it as a constant, but not write it as a constant.

Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Holding ArthurHolding Arthur

982317

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
  $endgroup$
  – Yves Daoust
  1 hour ago
  
  
  

  
  
  
  

add a comment | 

0

$begingroup$

Well, it really depends. In Chinese schools, students are told that $100%=1,40%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.

However, it is agreed around the world that you should not write something like "$250%$ liters of water".

So it is a good idea to think of it as a constant, but not write it as a constant.

Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Holding ArthurHolding Arthur

982317

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
  $endgroup$
  – Yves Daoust
  1 hour ago
  
  
  

  
  
  
  

add a comment | 

$begingroup$

Well, it really depends. In Chinese schools, students are told that $100%=1,40%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.

However, it is agreed around the world that you should not write something like "$250%$ liters of water".

So it is a good idea to think of it as a constant, but not write it as a constant.

Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Holding ArthurHolding Arthur

982317

$endgroup$

share|cite|improve this answer

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Holding ArthurHolding Arthur

982317

edited 1 hour ago

J. W. Tanner

2,3611117

edited 1 hour ago

J. W. Tanner

2,3611117

answered 1 hour ago

Holding ArthurHolding Arthur

982317

answered 1 hour ago

Holding ArthurHolding Arthur

982317

0

$begingroup$

I believe you can think of it both ways.

It’s a symbol for “parts of a hundred” that happens to have a constant value behind it, and at the same time it’s a constant that happens to have a symbolic meaning behind it.

share|cite|improve this answer

answered 1 hour ago

Victor S.Victor S.

31119

$endgroup$

add a comment | 

0

$begingroup$

I believe you can think of it both ways.

It’s a symbol for “parts of a hundred” that happens to have a constant value behind it, and at the same time it’s a constant that happens to have a symbolic meaning behind it.

share|cite|improve this answer

answered 1 hour ago

Victor S.Victor S.

31119

$endgroup$

add a comment | 

$begingroup$

I believe you can think of it both ways.

It’s a symbol for “parts of a hundred” that happens to have a constant value behind it, and at the same time it’s a constant that happens to have a symbolic meaning behind it.

share|cite|improve this answer

answered 1 hour ago

Victor S.Victor S.

31119

$endgroup$

share|cite|improve this answer

answered 1 hour ago

Victor S.Victor S.

31119

answered 1 hour ago

Victor S.Victor S.

31119

answered 1 hour ago

Victor S.Victor S.

31119

0

$begingroup$

I don't think it has a universally agreed nature.(Symbol,constant,or Unit, or else?) Even though it might have had a single nature at the moment it was created, after a long time usage by people, with non-mathematicans as the majority, its nature might be different among different people's point of view.

In my opinion, I would regard '%' equivalent to the phrase 'out of 100'. That means 15% is read as '15 out of 100' . However, I am pretty sure someone else will have his own interpretation on '%' which leads no contradiction to mine.

share|cite|improve this answer

answered 1 hour ago

Anson NGAnson NG

20819

$endgroup$

add a comment | 

0

$begingroup$

I don't think it has a universally agreed nature.(Symbol,constant,or Unit, or else?) Even though it might have had a single nature at the moment it was created, after a long time usage by people, with non-mathematicans as the majority, its nature might be different among different people's point of view.

In my opinion, I would regard '%' equivalent to the phrase 'out of 100'. That means 15% is read as '15 out of 100' . However, I am pretty sure someone else will have his own interpretation on '%' which leads no contradiction to mine.

share|cite|improve this answer

answered 1 hour ago

Anson NGAnson NG

20819

$endgroup$

add a comment | 

$begingroup$

I don't think it has a universally agreed nature.(Symbol,constant,or Unit, or else?) Even though it might have had a single nature at the moment it was created, after a long time usage by people, with non-mathematicans as the majority, its nature might be different among different people's point of view.

In my opinion, I would regard '%' equivalent to the phrase 'out of 100'. That means 15% is read as '15 out of 100' . However, I am pretty sure someone else will have his own interpretation on '%' which leads no contradiction to mine.

share|cite|improve this answer

answered 1 hour ago

Anson NGAnson NG

20819

$endgroup$

share|cite|improve this answer

answered 1 hour ago

Anson NGAnson NG

20819

answered 1 hour ago

Anson NGAnson NG

20819

answered 1 hour ago

Anson NGAnson NG

20819

0

$begingroup$

The percent sign is an abbreviation: just substitute "$color{red}%$" by "${}color{red}{cdotfrac{1}{100}}$", that's all. So for example: $15color{red}{%}=15color{red}{cdotfrac{1}{100}}=0.15$. Or the other way round: $1.23=123color{red}{cdotfrac{1}{100}}=123color{red}{%}$.

share|cite|improve this answer

answered 1 hour ago

Michael HoppeMichael Hoppe

11.1k31836

$endgroup$

add a comment | 

0

$begingroup$

The percent sign is an abbreviation: just substitute "$color{red}%$" by "${}color{red}{cdotfrac{1}{100}}$", that's all. So for example: $15color{red}{%}=15color{red}{cdotfrac{1}{100}}=0.15$. Or the other way round: $1.23=123color{red}{cdotfrac{1}{100}}=123color{red}{%}$.

share|cite|improve this answer

answered 1 hour ago

Michael HoppeMichael Hoppe

11.1k31836

$endgroup$

add a comment | 

$begingroup$

The percent sign is an abbreviation: just substitute "$color{red}%$" by "${}color{red}{cdotfrac{1}{100}}$", that's all. So for example: $15color{red}{%}=15color{red}{cdotfrac{1}{100}}=0.15$. Or the other way round: $1.23=123color{red}{cdotfrac{1}{100}}=123color{red}{%}$.

share|cite|improve this answer

answered 1 hour ago

Michael HoppeMichael Hoppe

11.1k31836

$endgroup$

share|cite|improve this answer

answered 1 hour ago

Michael HoppeMichael Hoppe

11.1k31836

answered 1 hour ago

Michael HoppeMichael Hoppe

11.1k31836

answered 1 hour ago

Michael HoppeMichael Hoppe

11.1k31836

0

$begingroup$

No, take for example $20 + 50%$. This is equal to $30$, while $20 + 50 cdot 0.01 = 20.5$

share|cite|improve this answer

answered 15 mins ago

PaulPaul

1,642910

$endgroup$

add a comment | 

0

$begingroup$

No, take for example $20 + 50%$. This is equal to $30$, while $20 + 50 cdot 0.01 = 20.5$

share|cite|improve this answer

answered 15 mins ago

PaulPaul

1,642910

$endgroup$

add a comment | 

$begingroup$

No, take for example $20 + 50%$. This is equal to $30$, while $20 + 50 cdot 0.01 = 20.5$

share|cite|improve this answer

answered 15 mins ago

PaulPaul

1,642910

$endgroup$

share|cite|improve this answer

answered 15 mins ago

PaulPaul

1,642910

answered 15 mins ago

PaulPaul

1,642910

answered 15 mins ago

PaulPaul

1,642910