🔢 Round It Right! Mastering Estimation with d.p. & s.f.

Ever stared at a calculator display packed with digits? Estimation swoops in to make numbers clear and comparisons quick. By mastering rounding to decimal places (d.p.) and significant figures (s.f.), you boost speed, reduce errors, and earn precious marks in O-Level exams.

The Core Idea

When rounding, we keep a number to a chosen level of accuracy and **replace the rest with zeros (or trim them)**. For decimal places, we count digits after the decimal point; for significant figures, we count from the first non-zero digit.

If the next digit is $\ge 5$ , round **up**.
If the next digit is $\le 4$ , round **down**.
d.p. focuses on place value after the decimal: e.g. 2 d.p. means two digits after the decimal.
s.f. ignores leading zeros: 0.003456 to 2 s.f. is 0.0035.

Worked Example: Fuel Economy Check

Problem: A car travels 457.386 km using 36.847 L of petrol. (a) Round the distance to 1 d.p. and 3 s.f. (b) Estimate the fuel economy, km/L, using your rounded values to 2 s.f.

Step 1: 1 d.p. for distance: look at 2nd d.p. digit in 457.386 → 8 $\ge 5$ , so
$457.386 \approx 457.4 \text{ km}$
Step 2: 3 s.f. for distance: digits are 4,5,7; next digit 3 $<5$ , so
$457.386 \approx 457 \text{ km (3 s.f.)}$
Step 3: Round fuel to 2 s.f.: 36.847 → first two significant digits 3,7; next digit 6 $\ge 5$ ,
$36.847 \approx 37 \text{ L}$
Step 4: Estimate economy using 457 km and 37 L:
$\dfrac{457}{37} \approx 12.35 \text{ km/L}$
→ to 2 s.f.
$12 \text{ km/L}$

Practice rounding daily—prices at the supermarket, distances on road signs, or scores in games. **The more you estimate, the faster and more accurate you become on exam day!**