3.4Approximation Errors

When calculations have multiple steps, rounding too early can cause errors to accumulate. These are called premature rounding errors.

Avoiding premature rounding errors

The area of a circle is 54 cm². Find its circumference, correct to 3 s.f.

Show solution▾

Area:

\pi r^2 = 54

r^2 = \frac{54}{\pi}

, so

r = 4.14593\ldots

Keep that in the calculator. Circumference

= 2\pi r

= 26.0

cm (to 3 s.f.)

Now round

r

4.15

first:

2\pi \times 4.15 = 26.07\ldots

, which gives

26.1

cm.

26.0

and

26.1

are different answers, and only the first is right.

Round once, at the end, to the accuracy the question asks for.