# Mental currency conversions

Hi all,

Are there any shortcuts to currency conversions? An example of what’s needed is a dollar = 0.63 Euro. This fluctuates and can be 0.62 one day and 0.64 another. 0.65 is relatively easy as it is equal to 13/20. I will need to covert the other way too, ie 1 Euro = 1/0.63 dollars.

If it’s just for your day-to-stuff whilst on vacation, why not simply use two thirds instead? The “other way around” is then just adding half on top.

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Thanks Bjoern, I actually do use 2/3 as an approximation. It would be nice to be a little more accurate if possible.

A couple of years ago I developed a system for currency conversions, where you essentially split the step into two rules:

For example, today to convert between Norwegian Krone and US Dollars, you have to divide by 8.8451.

If you simply add on 1/8 of the amount, and divide by 10, you get a very accurate answer.

Example: convert NOK 40 to USD:

40 ÷ 8 = 5.
40 + 5 = 45
45 ÷ 10 = \$4.50
[The exact answer would be \$4.52]

I’ve even made a tool (currency math rules generator) that helps generate these rules—maybe it can help you with finding a rule for the ones you need to do.

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Thanks Daniel, can you explain how you arrive at your approximations? Is it a set algorithm?

Correct me if I’m wrong, @Daniel_360 :

1/8.8451 = 0.11305… which is approximately 1.125/10, which is (1 + 1/8)/10

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I mean generally, a shortcut in this context means sacrificing accuracy for speed. I’m not sure what your definition of a shortcut is, but for me it needs to be faster than saying “Hey Siri, how much if 14 EUR in AUD.”. Also, I usually work with EUR 20.00 when something costs 19.95, so it really depends on the context… that’s why I said

Anyways, as far as more accuracy with little effort… just stick to a) moving decimal points and b) doing doubles and halves. Let’s start with

Let’s say I got 14 dollars that I want to convert to euros. I already know that 10% of 14 is 1.4; so we can easily get to 0.6 by taking half of 14 and adding 10% to it (i.e., 7 + 1.4 = 8.4). To get to 0.65, you can either add 10% of that 7 which was 50% and 10% of that will be 5% or you take half of the 10% you also already “calculated.” Done… and might I add, easier than doing 13/20.

Say you want 0.63 instead… 3 is half of 6, so you can just take half of your 0.6 result, move the decimal point and add it on top. For 0.62 it’s double of the 10% you calculated along the way and move the decimal point to add 2%.

### To summarize for anything between 0.6 and 0.66

You have amount X in AUD and you want to know how much that is in EUR. The first thing you do is calculate 0.6 by taking half and adding 10%. Let’s say X = 84, so you got 42 as your half and 8.4 as your 10% for 42 + 8.4 = 50.4 which according to you

would easily serve as a lower bound. Now, simply add 10% of this result to itself to get 0.66 as you upper bound for 50.4 + 5.04 = 55.44 and depending on what you’re trying to do here, you’re either happy with the fact that your AUD 84 will be somewhere between EUR 50.40 and EUR 55.44 or you do another step…

To get 0.61 or 0.65 you add or subtract 1/10 of the known 10% of the original amount (AUD 84) to or from the lower or upper bound, respectively*. For 0.62 or 0.64, you first double the original amount then do the same thing. Finally, for 0.63 you take half of your lower bound and add it after shifting the decimal point.

*or stick with the 10% of 50% method from earlier for 0.65

Stick with multiplication, EUR/AUD=1.59 and AUD/EUR=0.63 (at this very moment). So taking EUR 84 instead of AUD 84, you again do your 60% calculation, but then you add it to the original amount to get to 1.60 instead of 0.60 and then take off 10% of 10% and subtract it to get to 1.59

Just for ball parking if you take the inverse of the upper and lower bounds from about, you know that you can safely say that you’ll always be between 1.50 and 1.66, so once you got your lower and upper bounds for AUDEUR just add the original amount to your upper bound for the EURAUD upper bound and add half of the amount to the original amount to get your EURAUD lower bound.

I think that probably answers your question… maybe you could fill me in as to why you think you need the additional accuracy. It seems like overkill for the average traveller to be this accurate and/or this time sensitive.

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What about memorising the patterns of an abacus / soroban by linking them to your major system mnemonics?

@StopUserNameReuse are you sure you posted under the right topic?

Thanks Bjoern, that was perfect and I love the range system that you referred to in order to deal with fluctuations. As to the requirement for greater accuracy, I am contemplating moving to Europe and am interested in renting or potentially purchasing an apartment there, hence I need to know with some accuracy the associated costs.

Oh okay, I see… just keep in mind that not all places in Europe actually have the Euro and that cost of living expenses as well as taxation vary quite a bit in the individual countries that have the Euro… same is true for transportation and infrastructure cost.

…unless of course you already have a country in mind and just prefer to say “Europe” instead because it’s the Internet and all. Anyways, good luck with that then.