Numbers, Shapes & Proofs
The constants, shapes and terms worth actually knowing.
What is the value of pi to two decimal places?
The maths people genuinely use — in shops, kitchens, spreadsheets and news reports.
Most adults use a narrow slice of mathematics constantly and the rest of it almost never. That slice is percentages, averages, ratios and unit conversion — the arithmetic behind a discount, a recipe scaled for six, a mortgage rate or a statistic quoted on the news. This quiz stays inside that slice. There is nothing here requiring algebra or a calculator, but several questions cover the places where everyday reasoning reliably goes wrong, such as what an average does and does not tell you.
Every question in this quiz is listed below with its correct answer and the reasoning behind it. Play first if you would rather not see the answers — or read through as a study sheet.
Play it insteadAnswer: B. 50
Why: A quarter of 200. Percentages are just hundredths, so 25% means 25 parts in every 100.
Answer: A. £72
Why: Ten per cent of 80 is 8. Successive discounts do not simply add, which is why "20% off, then 10% off" is not 30% off.
Answer: D. The middle value when they are put in order
Why: The mean is the total divided by the count and the mode is the most common. Median resists distortion by extreme values.
Answer: C. 100
Why: The prefix "centi" means one hundredth. A kilometre is a thousand metres.
Answer: B. 1,000
Why: One millilitre occupies exactly one cubic centimetre, which is why recipes and syringes use both units interchangeably.
Answer: A. 90
Why: Four right angles make a full turn of 360 degrees. Two make a straight line.
Answer: D. £2.50
Why: Dividing by the count gives the unit price, which is the only reliable way to compare differently sized packs.
Answer: C. 16 metres
Why: Perimeter adds all four sides. Its area, by contrast, would be 15 square metres.
Answer: B. For every 2 of the first there are 3 of the second
Why: Ratios describe proportion, not absolute size, so 2:3 and 20:30 are identical.
Answer: A. 0.5
Why: One half is also 50%. Fractions, decimals and percentages are three notations for the same thing.
Most everyday numerical mistakes come from a handful of ideas nobody was taught properly. The useful core.
6 min readEach correct answer awards 10 XP. There is zero point penalty for incorrect guesses, encouraging learning through exploration.
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The constants, shapes and terms worth actually knowing.
What is the value of pi to two decimal places?
Geometry as it actually gets used — sides, angles, area and volume.
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