Rounding errors and inconsistent totals

I have a UK base site selling to retail customers. I have configured taxes for VAT at 20% and ticked the "Include this tax when displaying product prices" option.

Prices have been entered excluding tax. There is an item that sells for £20 inc VAT so the selling price is £16.66666

Generally everything works ok, but sometimes there are rounding errors and totals that do not add up.

When I add 630 of the items costing £20 to the cart, the total should be £12,600.00 but the total is £12,599.99 - is this just a fact of life? The only way I can see to fix this would be to enter prices including tax.

But there is a further problem: in the payment method pane on the checkout page it shows this breakdown that does not add up:

Subtotal: £10,500.00
Free Shipping: £0.00
Subtotal excluding taxes: £10,500.00
VAT: £2,100.00
Order total: £12,599.99

When I add 625 of the items costing £20 to the cart, the total is correct but breakdown on the checkout page is still wrong:

Subtotal: £10,416.66
Free Shipping: £0.00
Subtotal excluding taxes: £10,416.66
VAT: £2,083.33
Order total: £12,500.00

I tried setting the selling price of the item to £16.66667 and this seemed to improve things but when I add 1250 of the items costing £20 to the cart, the total should be £25,000.00 but the total is £25,000.01 but the breakdown was correct.