Knowledge Organiser: Rounding and Estimation
Key Terms
- Decimal places (d.p.): Number of digits after the decimal point
- Significant figures (s.f.): Meaningful digits starting from the first non-zero digit
- Estimation: Finding an approximate answer, usually rounding to 1 s.f.
- Truncation: Cutting digits off without rounding (different from rounding)
Must-Know Facts
- Look at the NEXT digit: 0 to 4 round down; 5 to 9 round up
- Leading zeros are NOT significant (0.0045 has 2 s.f.)
- Zeros between non-zero digits ARE significant (101 has 3 s.f.)
- Trailing zeros after a decimal point ARE significant (3.50 has 3 s.f.)
- For estimation: round everything to 1 s.f. first, then calculate
- 3.847 to 1 d.p. = 3.8; to 2 d.p. = 3.85; to 1 s.f. = 4
Key Methods
- Rounding to n d.p.: look at digit in position (n+1); round up if ≥ 5
- Rounding to n s.f.: start counting from first non-zero digit
- Estimation: round each value to 1 s.f., perform simplified calculation
- 0.005372 to 2 s.f. = 0.0054 (first two s.f. are 5 and 3)
Common Mistakes
- Counting leading zeros as significant: In 0.0045, the zeros are placeholders: only the 4 and 5 are significant (2 s.f.)
- Rounding in the wrong direction: Look at the digit after the one you are rounding: if it is 5 or more, round up; if it is 4 or less, round down
- Losing trailing zeros: A trailing zero after the decimal point counts as significant. 3.50 has 3 s.f., but 3.5 has only 2 s.f. So 3.50 is not the same as 3.5 when you are asked for a number of s.f.
- Estimation: not rounding to 1 s.f.: Round every value to 1 s.f. before estimating: rounding to 2 d.p. makes the calculation just as hard