Why 'sevenths' are easy to remember

I love being able to remember how to write fractions as a decimal. Most people think it's impossible to remember sevenths though - but it's quite easy if you know the pattern. When people say "Oh, about 2-in-7 people know their times tables", I can reply, almost straight away, "Hmmmm, that's around 28.57142857%"…

How does it work?

Well, all the sevenths (1/7, 2/7, 3/7 etc. all the way up to 6/7) are recurring decimals (that means they repeat after a while - in this case, 6 digits). Also, the only 6 digits they use are 1 4 2 8 5 & 7 - and it's always in that order.

If you put those 6 digits into 3 pairs, you get 14 28 57, where each pair is (very nearly) double the previous one (watch out for the '57'), and, to make it even easier, there's the link back to 7 - the first pair, 14, is double 7.

The decimal bit of each seventh just starts at a different place in that series of digits, works its way through…and then loops around again at the end.

So 1/7 starts at the beginning (best place to start), which happens to be the smallest digit ('1') with

    1/7 = 0.142857142857142857142857… (forever and ever)

2/7 starts at the 2nd smallest digit in there - the '2', so you get

    2/7 = 0.285714285714285714285714… (etc.)

3/7 starts at the 3rd smallest digit - the '4', giving

    3/7 = 0.42857142857142857142857… (ad infinitum)

And 4/7? Amaingly, that starts with the 4th smallest digit, which is '5' (you could remember that by thinking that 4/7 is just a little bit more than a half, which starts 0.5…)

    4/7 = 0.571428571428571428571428… (ad nauseam)

I'll leave 5/7 and 6/7 as an exercise for the reader :)

So I've bought one these Mares Puck dive computers and some Cetacea Absolutely Clear mask de-fog from Simply Scuba - we're off to Malta soon, and Jess & I plan to get away for a day or so under the waves. Louis might even do another BubbleMaker session - possibly in the sea, which will be one better than the pool session he had in Dubrovnik in the summer.

Jess & I did our PADI Open Water back in early May; Rob Randall took us through the training in the pool at Loddon Valley leisure centre, and the actual open water dives at Wraysbury Dive Centre - pretty murky, fairly cold (Jess was shivering, but then she hasn't made the same investment in pies as me). Nice bus though :)

I thought you might like to hear how I got on diving in Croatia (we stayed at the Valamar Club in Dubrovnik). We only managed 2 dives - guess I need better negotiating skills with certain other family members concerning the validity of diving on a family holiday.

The first dive was with the nearest hotel dive centre ('Abyss') was, in retrospect, pretty scary - just as well I went w/out Jess. They had PADI stickers up and everything, but no dive briefing, no emergency plan, no signals review, no equipment inspection, dive master didn't really speak English (and I don't speak Russian). The boat dropped us (I'd never dived off a boat before - that certainly added to the excitement) and then zoomed off to take other divers to other site (eek! all alone in the waves!).

Still, once underwater, things were a bit better (calmer, perhaps), but found it hard to keep up with the dive-master. Good site though (Grebeni, small reef), lots of fish etc. ~20min wait at the surface for boat.

For the second dive, I used padi.com to find another hotel dive centre ("Blue Planet", only 2mins further than first one). They seemed much more like my PADI training in UK - super safety aware, confident & relaxed. Met the dive master (Marko), discussed requirements (shallow dive for Jess), equipment check, detailed dive plan (from the shore, round 'Mala Afrika', Jess & I to return with one of the instructors, whilst others go further/longer/deeper). It was a much more relaxed dive, and I felt more secure with 1 guy leading, and 1 sweeping. Lots of beautiful fish, star fish, etc. Afterwards, we all met back at the benches and talked through the dive, what we saw, and learnt etc.

Both dives were the same price (340Kn ~ £40/each), but they could hardly have been more different.