Percentage Sign

[KWF]

I want to multiply $2500 by 6% without converting 6% to a decimal of 0.06.

Here is my solution: 6% X $2500 = $15,000%; now divide $15,000% by 100% to cancel out the percent sign (%) sign in $15,000%. The answer is $15,000/100 = $150.00

I wanted to think of the percent sign as a unit of measure. It needs to cancel out so that only the dollar sign was with the $150.00.

I wasn't sure whether to divide by 100% or multiply by (1/100)%.

1. Is this calculation mathematically correct?

2. Which is correct dividing by 100% or multiplying by (1/100)% or are both correct?

I know that this is a unconventional method, but I was curious to know whether or not the calculation is correct.

I thank you for your helpful comments.

 

[Bob Brown MSEE]

Here is my solution: 6% X $2500 = $15,000%; now divide $15,000% by 100% to cancel out the percent sign (%) sign in $15,000%. The answer is $15,000/100 = $150.00

$15,000% times 100 % = $1,500,000 (%)^{2
It is not the units that you wanted.}

 

[JeffM]

I want to multiply $2500 by 6% without converting 6% to a decimal of 0.06.

Here is my solution: 6% X $2500 = $15,000%; now divide $15,000% by 100% to cancel out the percent sign (%) sign in $15,000%. The answer is $15,000/100 = $150.00

I wanted to think of the percent sign as a unit of measure. It needs to cancel out so that only the dollar sign was with the $150.00.

I wasn't sure whether to divide by 100% or multiply by (1/100)%.

1. Is this calculation mathematically correct?

2. Which is correct dividing by 100% or multiplying by (1/100)% or are both correct? They obviously cannot BOTH be correct.

I know that this is a unconventional method, but I was curious to know whether or not the calculation is correct.

I thank you for your helpful comments.

If you want to think of percent as a unit of measurement (I am not sure that is completely valid) in the spirit of dimensional analysis, you need to think:

\(\displaystyle 100\% = 1 \implies 1 = \dfrac{1}{100\%}.\)

So your conversion factor to cancel percent must be \(\displaystyle \dfrac{$15,000\%}{1} * \dfrac{1}{100\%} = \dfrac{$150}{1} = $150.\)

For the life of me I cannot see any advantage in that process.

 

[KWF]

If you want to think of percent as a unit of measurement (I am not sure that is completely valid) in the spirit of dimensional analysis, you need to think:

\(\displaystyle 100\% = 1 \implies 1 = \dfrac{1}{100\%}.\)

So your conversion factor to cancel percent must be \(\displaystyle \dfrac{$15,000\%}{1} * \dfrac{1}{100\%} = \dfrac{$150}{1} = $150.\)

For the life of me I cannot see any advantage in that process.

Thanks JeffM for the reply!

Isn't dividing $15,000% by 100% the same as \(\displaystyle \dfrac{$15,000\%}{1} * \dfrac{1}{100\%} = \dfrac{$150}{1} = $150?\)

 

[JeffM]

Thanks JeffM for the reply!

Isn't dividing $15,000% by 100% the same as \(\displaystyle \dfrac{$15,000\%}{1} * \dfrac{1}{100\%} = \dfrac{$150}{1} = $150?\)

Yes, dividing by \(\displaystyle a\) is the same as multiplying by \(\displaystyle \dfrac{1}{a}\).

I showed it the way I did because dimensional analysis is usually presented in terms of multiplication (probably because a computation involving multiple conversions would make for a very confusing fraction).