Square of a Hundred Percent

Algebra Level 1

$\Large \left( \color{#3D99F6}{100 \%} \right)^{\color{#D61F06}{2}} = \ ?$

1% 100% 10000% 10%

42 solutions

Kanishk Bhatia
Aug 8, 2015

Always remember that when dealing with percentages , the notation x% means x/100. So here, 100% means 100/100 = 1. When you square 1, you get 1, which is again 100%.

hmmmm thanks

Muneeb Ahmad - 5 years, 8 months ago

nah the answer is still 100%

Mxolisi Sithole - 5 years, 5 months ago

thanks man...:)

Mahbubuzzaman Rakib - 5 years, 8 months ago

That make sense, thabk you

Viktor Christoffersen - 5 years ago

Thanks, I got it correct but for the wrong reasons. I had forgotten that percentages are fractions.

Andrew Ligon - 4 years, 9 months ago

100% does not necessarily = "1". We can have any number of something, and that same of number is 100% of whatever it is. If we have 100 times that original amount, in this case 100**2, then we have 10,000%. Maybe it's semantics, but I disagree with this answer.

Daniel Covino - 4 years, 9 months ago

Although 100 100 is greater than 10,000, obviously. So I misspoke. But if it were (100%) 2, the same concept would apply.

Daniel Covino - 4 years, 9 months ago

What about (1000%)² ,is it similar too as it is?

A Former Brilliant Member - 4 years, 9 months ago

Daniel Schnoll
Aug 13, 2015

If you have $1, then 100% of $1 is $1. So you have 1. Now, $1^2$ is still 1. Since 100% is 1, the answer is still 100%

what if u have 2$?

Jayant Choudhary - 5 years, 9 months ago

2 would be 200%. 100% is always 1. 200%^2 = 2^2 = 4 = 400%

David Roth - 5 years, 9 months ago

1 is not the value of the 100% in this case. Let's take for example if 1x=100%, then 2x=200% x could be any value. If x= 1$ then 1$=100%, and if x=2$, then 2$ would still be 100%. It doesn't really matter what is the value of x

Areia Ortíz - 5 years, 8 months ago

You cannot have more than 100%. You could say 2 was 2 times 1, or 2^2 is 4 times one, but there is no such thing as 200%

Logan Gaastra - 5 years, 8 months ago

@Logan Gaastra – suppose price of a ball was 2$. but now due to price hike of raw material, price of the ball got revised to 6$. what is the %hike in price of ball.

Answer is 200%. so there exists something like 200%.

Bikash Kumar - 5 years, 8 months ago

What if it is 2$?? ;-)

Nilabhra Mukherjee - 5 years, 10 months ago

100% of 100% of something is 100%

Andrew Riddle - 5 years, 8 months ago

x%=(x/100) so (200%)^2 =(200/100)X(200/100)=4=400%

Bikash Kumar - 5 years, 8 months ago

I got it now.....thanks man! :)

Tanmai PraTap - 5 years, 8 months ago

$2 = 100% = 1 (no units)

1^2 = 1 = 100% = $2.

Notice that 1 is not in $, but rather just an integer to represent 100% in decimal form.

Taylor Burnett - 5 years, 8 months ago

Yup right thanks!👍

Sumit Gaur - 5 years, 10 months ago

oooo... i see

izzati abdul hadi - 5 years, 10 months ago

good understanding

Faisal Maqbool - 5 years, 8 months ago

If somebody have $2 then ans would be 200%

Hemant Rohilla - 4 years, 8 months ago

Chung Kevin
Aug 5, 2015

$100 \% = 1$ .
$\left( 100 \% \right) ^2 = 1 ^2 = 1 = 100 \%$ .

I guess this 100% problem is going to be another usual question.

The AdamMZ - 5 years, 10 months ago

Do you like the problem?

Chung Kevin - 5 years, 10 months ago

No. Do I hate the problem? Not at all. I'm just all "meh". I mean, I guess this type of question is for new people.

The AdamMZ - 5 years, 10 months ago

@The Adammz – Yes, for those who are not completely familiar with percentages, this can be slightly surprising. Quite a lot of people got this wrong too, which means that they have to brush up on percentages.

Chung Kevin - 5 years, 10 months ago

i can t understand pls explain briefly

mathu mitha - 5 years, 10 months ago

100% = 100/100 = 1

After that, we square it.

The AdamMZ - 5 years, 10 months ago

factually this is - you are just assuming 100 next to 1 why ? I means 100% = 100/100 = 1 but this one will not be written as 1% Same as of your above equation .. if you break it down to 1 you can not assume 100% again !!

It may be difficult to understand what I written above with an example so let me give you an example.

in case of unknown value.

30/v x 100 = 100% applying square will make things different herer

900/v2 x 10000 = 100% ? Since we applied the square on only percentage side 100% will remain same ? no if it remains same it becomes and invalid equation !

Ubaid Rehman - 5 years, 9 months ago

% basically means 1/100, so 100%=100(1/100), which equals 1... whose square is 1... which is 100%

Antonio Arroyo Batista - 5 years, 9 months ago

% is always out of 100. So, 100% is 100/100. 1% is 1/100. 5% is 5/100. etc.

Radhika Saithree - 5 years, 9 months ago

with your equation squaring 100% remains the same.that is right.now understand with a simple example if you have 10 rupees you spend all.you spent 100%.If you have 100 rupees,you spend all.you spent 100%

Jamil Nizamani - 5 years, 9 months ago

Jajajaja this was a lot simpler than i thought

Gustavo Calderon - 5 years, 10 months ago

I failed because I though 100%= (100/100) * 100. So if ((100/100)*100%)^2 = ((1/1) *100)^2 = 10.000 Why in the explanations doesn't appear the 100 by which the ratio is multiplied in order to produce a value between 0 and 100?

Carlos Benítez - 5 years, 9 months ago

100%=100/100=1 or 100%=100*1/100=1 100%=(100/100) * 100 is incorrect

Jamil Nizamani - 5 years, 9 months ago

What am I doing wrong: (100%)^2 = (100/100 x 100/100) = (1 x 1) = 1% o.O Can someone explain it for me ?

Carlos Stefano - 5 years, 8 months ago

1 is 100% of 1, does that help?

Tord Hagervall - 5 years, 8 months ago

The part where you got it wrong is (1x1) = 1% It should be (100/100) x (100/100) = (1x1) = 1.00 = 100% Your final answer should convert the whole number into percentage and not having 1 (being 1%) as the final answer.

Junie Herrera - 5 years, 8 months ago

Observe que quando vc coloca cem sobre cem, desaparece o símbolo de porcentagem e ficam apenas números! Ora se multiplico e divido números o resultado vai ser APENAS um NÚMERO. O símbolo de PERCENTAGEM desapareceu quando vc colocou a fração 100/100. ?Compreendeu?

Antonio Araujo Correia - 5 years, 8 months ago

this is my opinion also ... the result will be 1%

Rana Hendawi - 5 years, 8 months ago

When you write 100/100, you changed the percentage into numerical form. You can't simply change the 1 to 1%, because you then just divided by 100

Elizabeth Wang - 5 years, 8 months ago

(1x1)=1, no 1%

Junio Cesar Ferreira - 5 years, 8 months ago

100 percent is 100 out of 100....now multiplying it with the same 100/100* 100/100 gives you just 1. with no unit. suppose we take 100% as 2 out of 2......now multiplying 2/2 * 2/2 also gives 1 so....how does it justify

Abhijeet Survase - 5 years, 8 months ago

Sorry myignorance= 100% of "something" can be 1, or 2, or 20...therefore the result may vary?

Eduardo Sorkin - 5 years, 8 months ago

Hey Eduardo, there can be only one answer which is 1. 100% is basically 100/100 but if you want to use 20 for example: 100% of 20 is also 20, so it is 20/20, which is still equal to 1. if you think the answer can be 20 for example, let's convert that to percentage.

20 = 20/1 = 2000/100 = 2000%

so 100% can't be a number other than 1.

Jb Cunanan - 5 years, 8 months ago

Brian Stanfill
Aug 13, 2015

If the math behind the solution seems complex, just test the multiple choices aloud. Only "100%" makes sense when you ask yourself, "What is all of 100%?"

Ishaan Srivastava
Aug 13, 2015

100% is equivalent to 1 as we all know when converting decimals and fractions to percentages and therefore when squaring 1 it is equal to its self and 1 is 100% in percentages so 100% is your answer

Bruno Po
Sep 11, 2015

Lots of people are asking "what if 100% is 2$?", "then wasnt it going to be 2$², 4$? 200%?, and so on? Doesnt it depend on what is 100%?"

No, it does not depend on what 100% is, 100% is only 2$ if it is 2$ from a total of 2$, so 2$/2$ = 1.

100$ is only 100% if it is 100$ out of 100$ so 100$/100$ = 1

And so on...

Arun Das
Aug 16, 2015

(100%)^2 = (100 x 1/100)^2 = 1^2 = 1 = 100 x 1/100 = 100%

Anny Ahmed
Aug 16, 2015

(100/100) 2 = 1......then 1 * 100/100 = 100%

David Edward
Aug 13, 2015

100% = 1.0 => (1.0)^2 = 1.0 => 100%

Ben Berger
Aug 8, 2015

$100\%^2$ = 100%*100%=100%

Mehnaj Hridi
Aug 7, 2015

100%=1 then, 1^2 =1=100%

Raakin Kabir
Sep 9, 2016

100% = 1 100%^2 = 1^2 100?^2 = 1 * 1 = 1

M.Ahsaf Abid
Jul 29, 2016

$100\%$ means $\frac{x}{100}$ . So $100\%$ means $\frac{100}{100}$ = $1$ . Thus squaring 1, you will get $1$ which is $100\%$ .

Charlotte Yates
Feb 1, 2016

100% as decimal probability is 1.0

1 x 1 = 1 = 100%

James D
Dec 22, 2015

100%=1 therefore 1^2=1=100% hope you understand

Sina Nakhkoob
Oct 23, 2015

Most people would get fooled by this problem, but it's actually quite simple. Since 100% = 1, then (100%)^2 = 1^2 = 1 ==> 100%

Dick Guertin
Oct 21, 2015

What people may be missing is that to do the math, you must convert the percent to a pure fraction, square the fraction, and then convert back to a percent. For example, 90% is 90/100, which when squared is 8100/10000 which is 81/100 or 81%. Likewise, 100% is 100/100 which squared is 10000/10000 which is 100/100 or 100%

Mark Tebbit
Oct 15, 2015

100% means 'the whole of'. That's all you need to know.,

Jake Williams
Oct 14, 2015

The correct way to think of percentages is as probabilities. To square a percentage you have to convert to a decimal probability, square that value, then convert back to percentage. 100%=>1.00 1.00^2=1.00 1.00=>100% Remember, percentages are just a way of writing probabilities.

Shaheryar Waris
Oct 7, 2015

% means (1/100) so 100% = 100(1/100) which is equal to 1 and square of 1 is 1 also 100%=1 so square of 100% is also 100%

Usama Ejaz
Oct 4, 2015

the formula of percentage is ( obtain amount / total amount ) * 100. if the answer is 100% then it means both obtain amount and total amount are same e.g. ( 50/ 50 ) * 100 or ( 63.5 / 63.5 ) * 100. in every case the answer will be 1 because both numerator and denominator are same. so 100% means 1 then 100% ^ 2 means 1 ^ 2 which is also equals to 1. so it means that 100% ^ 2( or whatever the power is e.g. 3, 4 , 50) is 100%.

John Knight
Oct 2, 2015

\sqrt{100%}=\sqrt{1.00}=1; hence 1 ^{2}=1 or 1.00=100%: We assume the spuare of (x); i.e. 100% of a whole of any quantity, thus \sqrt {100%} is the same as \sqrt {1.00}, which is 1. If we square 1, i.e., 1^{2}, it equals 1; 1.00-or 100%. Again (in terms of a percentile), 1=1.00=100%; interestingly 1.00X1=1 (this a calculator's output).

William Adams
Oct 1, 2015

100% is always 100% regardless of the amount attached to it. 100% written in decimal form is 1.00 90% written in decimal form is 0.90 etc... I will use 2 examples.

100% of 50 is 50. So the equation can be written as 50/50 or 50 out of 50.
50 divided by 50 is always 1. Therefore (100%)^2 = (50/50) (50/50) = 1.00 1.00 = 1.00 or 100%

For the next example I will illustrate when a percentage is squared that is NOT 100%

90% of 100 is 90. So this can be written as 90/100 or 0.90. 90% written in decimal form is 0.90 Therefore (90%)^2 = (90/100) (90/100) = 0.90 0.90 = 0.81 or 81%

Ivan Stewart Saldajeno
Sep 22, 2015

One should remember that 100%=1. The solution will follow.

Garvin Goei
Sep 20, 2015

100% is equal to 1, so (100%)^2 means 1^2 = 1. Convert 1 to percentage, becomes 100%. Done!

Steve Rae
Sep 17, 2015

Be nice to the new guy, I had to do some thinking about that. I'm way out of practice.

Juju Camargo
Sep 14, 2015

100% =1, 1 ao quadrado=1, logo só Pode ser 100%

Hadia Qadir
Sep 12, 2015

100 % )^ 2

= ( 100/100 ) ^2

= (1) ^ 2

= 100/100

= 100%

Yuva Raj
Sep 11, 2015

if 100%=1, 1*1=1, thus 100% square=100%

Tootie Frootie
Sep 5, 2015

it's how we started the question

Eduardo Maia
Aug 21, 2015

100/100^2=1=100%

Adith A Danthi
Aug 17, 2015

100%=100/100=1 1^2=1=100%

Sonal Singh
Aug 16, 2015

100% = 100/100 =1, (100%)^2 = 100/100 100/100 = 1 1 =1, 100%=(100%)^2

Ali Fleih
Aug 16, 2015

One has to know that 100% is actually just...one.

Nishu Mashruwala
Aug 16, 2015

100% is the same as 1. So if you plug in 1 to the expression in place of 100%, you see 1^2. 1^2 = 1 x 1. 1 x 1 = 1. Since 1 is not an option as an answer, you have to convert back to percent. 1 is the same as 100% so my answer is 100%.

Zaman Ahsan
Aug 15, 2015

x% = x/100 so 3%=3/100 (for example) then 100%=100/100 =1 now (100%)^2 = (100/100)^2 =1

make math easy...

Javed Hasan
Aug 15, 2015

100%^2 = (100/100)^2=1^2=1=1*100/100=100%

Farjad Shahid
Aug 13, 2015

(100%)^2 = (100/100)^2 = (1)^2 = 1 = (1*100) = 100%

Raven Mendoza
Aug 13, 2015

The easiest question i would have on a test

Alam J
Aug 13, 2015

% is something a part of 100. So,100% is 100 out of 100 or 1 out of 1. 1 sq is 1, that is again in % is 100%

Eury Luna-filho
Aug 13, 2015

I have made the same reasoning as Ishaan Srivastava!

Rebekah Radcliffe
Aug 12, 2015

You can't have more than 100%

You can have more than 100%, you could have, for instance, a 240% rise in sales compared to the quarter before, if you were a business, for example.

Kyle Fairns - 5 years, 10 months ago

Sure, no body said 100% percent is the limit but that is the rule. If you want to know what a product would cost with a 240% rise, you would multiply the original ammount by 240/100=2.40 times the original amount, for example.

Guido Aggeler - 5 years, 7 months ago

Square of a Hundred Percent

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