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Choosing Between Mental, Written and Calculator Methods

The same calculation can make one method sensible and another needlessly difficult. Open Full Article...

Surds and Exact Values: Keeping Roots Exact

If √2 is about 1.414, why would a mathematician sometimes prefer to leave the answer as √2? Open Full Article...

Calculating with Upper and Lower Bounds

If a length is written as 8 cm to the nearest centimetre, does that prove the real length is exactly 8 cm? Open Full Article...

Applying the Order of Operations Correctly

Why does 2 + 3 × 4 equal 14 rather than 20, even though both calculations look possible? Open Full Article...

Indices, Roots and Fractional Powers Explained

Why does 2³ mean 2 × 2 × 2, while 2^(1/2) extends the same power notation through a connection with roots? Open Full Article...

Standard Form and Orders of Magnitude

The numbers 7,200,000,000 and 0.0000000072 contain almost the same significant digits but represent vastly different scales. Open Full Article...

Efficient Mental Calculation Strategies

Two different-looking calculations, 299 + 458 and 300 + 458 − 1, both equal 757. Open Full Article...

Prime Factors, Multiples and Divisibility

What makes 24 a factor of some numbers but a multiple of others? Open Full Article...