Category: math

Math: break-even year-over-year

Self-tutoring about math: the tutor mentions perhaps an oft-considered question. Suppose an investment loses x% this year. What percent does the resulting sum need to gain next year in order to break even? Imagine an investment of initial value $250.

Calculator use: when adding isn’t associative(?)

Tutoring math, curiosities can arise. The tutor mentions a calculator one. In front of me are two reliable scientific calculators from different manufacturers. Both give the following results: 2+1exp20-1exp20 = 0 but 2+(1exp20-1exp20)=2 1exp20 means scientific notation: 1×1020. How can

Math: idempotent

Tutoring math, terms can be interesting. The tutor mentions idempotent. idempotent (adj): repeatable without further result, or unchanged by repetition of an operation. Source: encylopediaofmath.org

Math: bacon and eggs

Tutoring math, you face real-life scenarios. The tutor mentions an example. Suppose one egg and two strips of bacon contain 13.5g protein, but two eggs and one strip of bacon contain 16.5g protein. How much in each? Let x be

Math: increase then decrease by same percentage, or vice-versa

Tutoring math, you run into curiosities. The tutor mentions one with percentage. If an amount is increased, then decreased, by the same percentage, the net effect is shrinkage, regardless of which happens first. Let the amount be 100. Furthermore, for

Math: ratios: making oatmeal: 4:9

Self-tutoring about ratios: the tutor reflects about preparing oatmeal. The ratio of oatmeal to water, with the brand I use, is 1 and 1/3 cup to 3 cups. As such, it’s a less convenient ratio to scale up or down

Metric system: how big is a hectare?

Tutoring science, the metric system may arise. The tutor mentions the definition of a hectare. hectare (noun): a square unit spanning 10000m2. A hectare can be pictured an as area 100m wide by 100m long. Another way to imagine a

Calculator usage: negative numbers to rational exponents (with odd roots)

Tutoring high school math, scientific calculators are a permanent fascination. The tutor mentions a quirk many might share. Due to and the fact that a common exponent notation is xa=x^a, it follows that (-8)^(2/3)=4. Curiously, of all the calculators in

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Spreadsheets: Excel: the pi() function

Tutoring math, your curiosity naturally extends to spreadsheets. The tutor points out a neat feature of Excel. If you type =pi() in a cell, the value of π will appear. I find that 14 decimal places are available. Source: www.math.com

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Math, engineering, trades: steepness measurement: definition of grade

Tutoring math, you encounter grade. The tutor discusses its definition and why it might be surprising. Grade is defined as 100%*(vertical/horizontal). In the above diagram, it would be as follows: grade=100%*(rise/run). By itself, rise/run is called slope. Therefore, grade=100%*slope What

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