Notes
How the tools are built and checked, and the occasional piece on the numbers behind them.
One month after the 31st There is no 31 February, so a month has to land somewhere. Which somewhere is a rule, not a fact. Accuracy before speed: why raw WPM flatters you Ninety-two per cent accuracy at 60 raw is 55 net. The errors cost more than the speed earns. Why your PDF will not shrink A scanned contract halves. A forty-page report barely moves. The difference is what is inside the file, not how hard you compress it. Morse speed is measured with one word: PARIS PARIS is exactly 50 units of Morse. Divide by that and words per minute becomes milliseconds per dot. Halving a recipe that calls for three-quarters of a cup Three-eighths of a cup is six tablespoons. The awkward halves all have a clean answer in a smaller unit. What two more years on a car loan actually cost Stretching $28,000 from 60 months to 84 saves $131 a month and costs $2,558 in interest — and that is the smaller problem. American recipes in a European oven Every US baking temperature converts to an untidy Celsius figure, and then the fan takes another twenty degrees off. Picking a name in front of a room The draw has to be fair and it has to look fair to thirty people at the back, and those are different design problems. Choosing an activity multiplier you will not regret One band is worth 282 calories a day. That is more than half the deficit most people are trying to run. The two weeks a year when your recurring meeting moves London and New York are five hours apart, except for three weeks in spring and one in autumn, when they are four. Which barcode do you actually need? Retail codes are issued numbers you have to own. Internal codes are free text you invent. Choosing wrongly is expensive in one direction only. Why Windows will not open your iPhone photos HEIC is half the size of JPEG for the same picture. The reason nothing else reads it is licensing, not quality. Why an emoji is four bytes A is one byte, é is two, and a grinning face is four. The pattern is visible in the binary if you know where to look. Two dice are not one bigger die 2d6 and a d11 cover almost the same range. One of them rolls the middle six times as often. Grade, angle and ratio: three ways to write one slope A 100% grade is 45 degrees, not a vertical wall. The three notations are not interchangeable and all three are on the signs. Why a calorie deficit stops working after a few months The target you set at 75 kg is a smaller deficit at 65 kg. The arithmetic moves under you while the number stays still. A raise into the next bracket cannot leave you worse off Only the money above the line is taxed at the higher rate. The whole salary never is. How every calculator gets checked before it ships Boundaries, locales and a 375-pixel phone. The three checks every tool passes. Speed limits in the other unit, and the speedometer that flatters you A converted limit is never a round number, and your speedometer is legally allowed to be wrong in one direction. How big to print a QR code The working rule is scanning distance divided by ten. Everything else follows from how many modules the payload needs. Choosing a page size for scans and screenshots A screenshot on A4 is a small picture in a large white field. Fitting the page to the image is usually the better answer. Anagrams, subsets, and which dictionary you are playing against LISTEN gives SILENT, ENLIST and TINSEL. Whether it also gives TELSON depends entirely on the word list. Mean, median or mode: which average to report Three answers to one question, and the gap between them is the most informative thing about your data. Why random picking keeps missing the same people Draw thirty names from a class of thirty and about eleven of them never come up. That is not a broken picker. What has to be on an invoice The EU sets a common list. The United States sets almost nothing. Both make the same document look wrong to the other. Why 2.2 is not enough Rounding a conversion one step too early is the most common bug in this category. A ten-degree rise is not fifty degrees Temperature is the one conversion with an offset, and the offset does not apply to differences. Why BMI misreads tall people, short people and athletes The formula divides by height squared. Bodies scale closer to a cube, and the gap grows with height. Building a nine-step scale from one brand colour Nine tints of one hue, and only two of them can carry body text on white. Knowing which two is the whole job. Resize first, compress second Dimensions are most of a file. Going from 3000 pixels wide to 1200 removes six sevenths of the data before the quality slider does anything. The character limits that actually truncate Some limits reject your text, some silently cut it, and one of the most quoted is measured in pixels rather than characters. Why calculators disagree about minus two squared Some answer −4 and some answer 4. Both are following a rule, and the rules are different. Let it decide, then watch your own reaction The answer is not the useful part. What you feel in the second after it lands is. Has your salary kept up with prices? A raise that beats zero is not the same as a raise that beats inflation. The test takes one division. Reading an amortisation schedule What the first twelve rows tell you that the monthly payment does not. Two gallons, and two mpg figures that do not compare A British 40 mpg car and an American 40 mpg car are not the same car. The gallons are 20 per cent apart. The medium field decides where your traffic lands Analytics groups channels on one parameter. Get it wrong and the campaign shows up as unassigned, which is a report nobody reads. 5K, 10K and the pace table runners actually need Converting the distance is easy. Converting the pace is where the arithmetic goes backwards. Volume, capacity, and the walls in between A 30 by 20 by 15 cm box is 9 litres of space and rather less than 9 litres of storage. Running a prize draw you can defend afterwards Being fair is the easy half. Being able to show you were fair, a week later, to someone who did not win, is the other one. Where the 4% rule comes from, and what it assumes It is a finding from one study of one country’s history, and it answers a narrower question than it is usually asked. Per cent and percentage points are not the same thing A rate moving from 4% to 5% rose by one point and by twenty-five per cent. Both are true and they are not interchangeable. Ads, and where they are not Why nothing sits above the tool, and what that costs. A real coin is not quite fair A flipped coin lands the way it started about 51% of the time. The bias is in the physics, not the metal. The two-by-four is not two by four Some measurements are names rather than dimensions. Converting them gives an exact answer to the wrong question. The year your money starts earning more than you put in There are two crossover points in a savings plan, twelve years apart, and only one of them feels like anything. 23 kg or 50 lb: the two numbers airlines weigh you against They are not the same limit. One is 2 kg more generous than the other, and which one applies depends on the ticket, not the airport. When two cycles line up again Buses every 12 and 18 minutes meet every 36. The lowest common multiple is a scheduling tool before it is a maths exercise. What to tip, by country The percentage is the easy part. Whether a tip is expected, insulting or already on the bill is the part that varies. Why aircraft still measure height in feet Cruising altitude is 35,000 ft, which is 10,668 m. The tidy number sits on the imperial side, and that is not an accident. APR and the interest rate are different numbers One prices the borrowing. The other prices the deal. A $750 fee moves them 1.3 points apart. Dutch and German are longer Designing a layout that survives a 30% expansion. Turning a decimal inch into a mark on the tape Converters answer in decimals. Tape measures are marked in sixteenths. This is the step in between. Why your lender quotes a higher payment than the calculator Principal and interest is one of four numbers on the bill. The other three are where the surprise lives. Loading a barbell when the plates are in the wrong units A 45 lb plate is 20.41 kg. Every round number in lifting is round in one system only.