Rounding Estimation And Bounds
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Rounding to a Given Place Value
- Identify the digit in the required place value, then count in that unit to find the two possible rounded values (one below, one above).
- Circle the digit immediately to the right of the required place; if it is 5 or more, round up; if less than 5, round down.
- For decimal places, ensure the answer has exactly the specified number of decimal places (e.g., 2.40 for 2 d.p., not 2.4).
- When rounding to a place value (e.g., nearest 100), fill any following places before the decimal point with zeros (e.g., 1567.45 → 1600).
Rounding to Significant Figures
- The first significant figure is the leftmost non-zero digit (e.g., 0.006207 → first s.f. is 6).
- Count digits from the first s.f. to locate the required s.f.; zeros between non-zero digits are significant.
- Round using the same rules: circle the next digit; if ≥5 round up, else round down.
- For large numbers, fill with zeros up to the decimal point (e.g., 34 568 to 2 s.f. → 35 000).
- For decimals, insert zeros between decimal point and first s.f. as needed (e.g., 0.003 435 to 3 s.f. → 0.003 44).
- Unless stated otherwise, give final answers to 3 significant figures; in money use 2 d.p.; in angles use 1 d.p.
Estimation
- Estimate by rounding each number to 1 significant figure (or a convenient value) before calculating.
- Avoid rounding small numbers to zero, especially in denominators (division by zero is undefined).
- For addition/multiplication: rounding both numbers up gives an overestimate; rounding both down gives an underestimate.
- For subtraction/division: rounding the first number up and the second down gives an overestimate; the opposite gives an underestimate.
- Estimation is useful for checking if an exact answer is reasonable.
Upper & Lower Bounds
- Bounds describe the range a rounded number can lie between: lower bound (LB) ≤ x < upper bound (UB).
- To find bounds: divide the degree of accuracy by 2, then add to get UB and subtract to get LB.
- Example: 3.6 km (1 d.p.) → degree = 0.1, half = 0.05 → LB = 3.55, UB = 3.65.
- The error interval is written as LB ≤ x < UB (e.g., 3.55 ≤ l < 3.65).
- Always identify the degree of accuracy correctly (e.g., nearest metre, 2 s.f., etc.).
Bounds on a number line
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1.Write 0.3728 correct to 1 decimal place.
Easy- A0.4
- B0.37
- C0.3
- D0.38
2.The height, h metres, of a tower is 128 m, correct to the nearest metre. Complete the statement about the value of h: ___ ≤ h < ___
Medium- A127.5 ≤ h < 128.5
- B127 ≤ h < 129
- C127.5 ≤ h ≤ 128.5
- D128 ≤ h < 129
3.Write 867 correct to the nearest ten.
Easy- A870
- B860
- C900
- D800
4.The length, l cm, of a pencil is 18 cm, correct to the nearest centimetre. Complete the statement about the value of l: ___ ≤ l < ___
Medium- A17.5 ≤ l < 18.5
- B17 ≤ l < 19
- C17.5 ≤ l ≤ 18.5
- D18 ≤ l < 19
5.Write 849.481 correct to 1 decimal place.
Easy- A849.5
- B849.4
- C849.48
- D850.0
6.Write 97.4236 correct to 3 decimal places.
Easy- A97.424
- B97.423
- C97.420
- D97.400
7.Write 3.72194 correct to 3 decimal places.
Easy- A3.722
- B3.721
- C3.720
- D3.700
8.Write 8379 correct to the nearest hundred.
Easy- A8400
- B8300
- C8000
- D9000
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