Decimal Places (d.p.)

Look at the digit directly after your cut-off. If 5 or more, round the previous digit UP.

Example: 3.47 to 1 d.p. → 3.5 0.124 to 2 d.p. → 0.12

1 Significant Figure (s.f.)

Keep only the first non-zero digit. Zeros at the start don't count!

Example: 382 → 400 0.0068 → 0.007

Estimating Calculations

Round every number to 1 significant figure first, then calculate.

Formula: Round → Calculate

Example: Estimate 39 × 5.1 ≈ 40 × 5 = 200

Money Estimates

Real-world checks: Usually round costs to the nearest whole pound.

Significant Figures vs Decimals

s.f. counts from the first non-zero digit. d.p. counts from the decimal point.

Example: 0.0053 is 2 s.f. but 4 d.p.

Rounding in Division

Round each number to 1 s.f. before dividing.

Example: Estimate 412 ÷ 19 ≈ 400 ÷ 20 = 20

Estimating Complex Expressions

Follow BIDMAS: Brackets, Indices, Division/Multiplication, then Addition/Subtraction.

Example: Estimate (48.7 × 11.2) ÷ 4.9 ≈ (50 × 10) ÷ 5 = 100

Deciding Accuracy

If a question specifies "reasonable accuracy", 1 or 2 s.f. is usually target.

Upper/Lower Estimates

To get the MAXIMUM estimate for a fraction, use the Upper Bound for the top and Lower Bound for the bottom.

Reasonableness

After estimating, ask: "Does this answer make sense?" If you estimated 40 × 5, the answer should be near 200, not 2000.