15% VAT - How to work it out from 17.5% inc prices

It appears a lot of people have been looking at my waffle on "Markup and Margins" page in order to convert prices from "inclusive of 17.5% VAT" to "inclusive of 15% VAT". By the way, if you're not in the UK, VAT = Value Added Tax and after many many years of it being 17.5%, it's just been changed to 15%. The government have said they will increase it again after one year.

So, if you want to know WHY the following calculations work, read about Markup and Margins - VAT is a Markup type of calculation. If you just want to know what to tap into your calculator or spreadsheet, here's what you do:

To convert a price from 17.5% inc VAT to 15% inc VAT - Multiply by 0.9787 (beware of rounding!)
Example: £117.50p x 0.9787 = £115.00

To convert a price including VAT at 17.5% to an Excluding VAT price - Divide by 1.175
Example: £117.50 / 1.175 = £100.00

To add VAT at 15% to an Excluding VAT price - multiply by 1.15
Example: £100 x 1.15 = £115.00

The dangers of rounding.
Currency is used with an accuracy of 2 decimal places, the smallest unit being £0.01 or 1pence. The exact result of £117.50 x 0.9787 is £114.99725. As we don't have a coin for 0.725 of a pence, we need to round up. Depending on when you round a number in a calculation, you can get an error that grows as you use that number in further calculations. To help prevent this you have two options,
1) you could multiply by a more accurate figure, like 0.97872340425531914893617021276596,
2) divide by 1.175 then multiply that answer by 1.15, which is the method I prefer as I find it easier to remember