Moving the Decimal Point

When you have a fraction, meaning you are dividing one number by another, you can always move the decimal point in both numbers, provided you move it the same number of places in each number (both numerator, and denominator), and in the same direction.

Now, when you are multiplying two numbers, you can always move the decimal point in both of them, provided you move it the same number of places in each factor, and in the opposite direction.

These two manipulations can significantly simplify the given operation.

Chords in a Circle

The diameter is the chord of maximum length. If the circle has a chord of length L, then the diameter cannot be less than L. The circle can be as large as we want but it cannot be too small. It has to be large enough so the chord of length L fits inside.