Rounding to d.p. and s.f.
d.p. counts after the decimal. s.f. counts from the first non-zero digit.
Decimal places (d.p.). Count digits AFTER the decimal point.
- to d.p.: look at 3rd d.p. () → round down → .
- to d.p.: look at 4th d.p. () → round UP → .
Significant figures (s.f.). Start counting at the FIRST non-zero digit.
- has s.f. ().
- has s.f. ( — trailing zero after decimal IS significant).
- has s.f. (trailing zeros in integers are AMBIGUOUS — usually or ).
- has s.f. (decimal forces all trailing zeros to count).
Rules:
- Leading zeros (before first non-zero) are NEVER significant.
- Zeros between non-zero digits ARE significant. ( has s.f.)
- Trailing zeros after a decimal ARE significant. ( has s.f.)
- Trailing zeros in integers are ambiguous — treat per context.
Round half up. When the digit being rounded is exactly , round UP.
- to d.p. → .
- to d.p. → .
Worked qualitative. Why is said to have s.f., not ?
- Significant figures convey ACTUAL PRECISION, not how many digits are written.
- The leading zeros just mark the place value (telling us this is a small number) — they don't add precision.
- Two non-zero digits = two significant figures.
Edexcel tip. Always state both numbers when rounding: 'Look at the next digit (); since /, round up/down'.
- d.p. counts after decimal.
- s.f. starts from first non-zero.
- Leading zeros: not significant.
- Trailing zeros after decimal: significant.
- Half UP for exact .