Approximate values and sensible estimation

2026-10-02Numbers & Estimation Mr Chan

Round to a required accuracy, estimate products and quotients, and check whether an answer is reasonable.

Key formulas

Nearest 10: \text{look at units digit}

Nearest 0.1: \text{look at hundredths}

Estimate: \text{round first}, \text{then calculate}

Rounding rules

To round to a stated place, look at the next digit. If it is 5 or more, round up; otherwise leave the digit unchanged. State the accuracy clearly: nearest 10, nearest 0.1, or 3 significant figures as required.

Estimation strategy

Before a long calculation, round each number to one or two significant figures and compute mentally. The estimate tells you the order of magnitude so a calculator slip stands out immediately.

Significant figures in context

Hong Kong junior secondary questions often ask for answers correct to 3 significant figures. Count from the first non-zero digit. Trailing zeros after a decimal point can be significant; trailing zeros in a whole number need care — prefer scientific notation when clarity matters.

Exam habit

Write the unrounded value, then the rounded answer on a separate line with the accuracy stated in words.

Worked example

Round then estimate

Problem. Estimate 197 × 48 by rounding each factor to 1 significant figure, then compare with the exact product.

Solution. 197 ≈ 200, 48 ≈ 50, estimate 200 × 50 = 10000. Exact 197 × 48 = 9456, which is close in magnitude — the estimate confirms the decimal place is sensible.

Review quiz

1 / 4

8472 to the nearest 100 is

Practice questions

Round 8472 to the nearest 100 and to 2 significant figures.
Estimate 48.7 × 19.2 by rounding each factor to 1 significant figure.
Round 0.003582 to 3 significant figures.

Study notes

Does 5 always round up?

In school exams, yes — round 5 up.

Why estimate before calculating?

An estimate catches wrong calculator key presses and misplaced decimal points.