Rounding Estimation And Bounds
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课程笔记
Rounding to Decimal Places
- Identify the digit at the required decimal place; look at the next digit to the right.
- If the next digit is 5 or more, round up (increase the digit). If less than 5, round down.
- Write the answer with exactly the required number of decimal places (e.g., 2.40 for 2 d.p.).
- Do not add extra zeros after the decimal place unless needed to show accuracy.
Rounding to Significant Figures
- The first significant figure is the leftmost non-zero digit.
- Count digits from the first significant figure to find the required significant figure.
- Use normal rounding rules; for large numbers, fill with zeros up to the decimal point.
- For decimals, fill zeros between decimal point and first significant figure (e.g., 0.00344 to 3 s.f.).
Estimation
- Round each number to 1 significant figure (or a convenient value) before calculating.
- Avoid rounding to zero, especially in denominators.
- For addition/multiplication: rounding up gives an overestimate; rounding down gives an underestimate.
- For subtraction/division: rounding numerator up and denominator down gives overestimate; opposite gives underestimate.
Upper and Lower Bounds
- Bounds are the smallest (LB) and largest (UB) values a rounded number can take.
- For a number rounded to a given accuracy, half the degree of accuracy is added/subtracted to find UB/LB.
- Error interval: LB ≤ x < UB (LB included, UB excluded).
- Example: 3.6 (1 d.p.) → LB = 3.55, UB = 3.65.
Bounds of 24 800 (nearest 100)
Calculations with Bounds
- For addition: UB = UB + UB, LB = LB + LB.
- For subtraction: UB = UB – LB, LB = LB – UB.
- For multiplication: UB = UB × UB, LB = LB × LB.
- For division: UB = UB ÷ LB, LB = LB ÷ UB.
Applying Bounds in Context
- To find maximum possible value, use upper bounds for quantities that increase the result and lower bounds for those that decrease it.
- To find minimum possible value, use opposite bounds.
- When counting discrete items (e.g., number of panels), round up for minimum needed, down for maximum possible.
- Always check whether the context requires rounding up or down (e.g., people, crates).
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练习题
免费预览——47 题中的 8 题。注册即可查看全部。
1.Write 0.046875 correct to 2 significant figures.
Easy- A0.047
- B0.046
- C0.05
- D0.0469
2.Write the number 0.076499 correct to 2 significant figures.
Easy- A0.076
- B0.077
- C0.0765
- D0.08
3.Calculate 2.38 + 6.42, writing down your full calculator display. Write your answer correct to 4 decimal places.
Easy- A8.8000
- B8.8
- C8.80
- D8.800
4.A bag of crisps weighs 150 g to the nearest gram. Complete the statement about the weight, w g, in the bag. ... ≤ w < ...
Easy- A149.5 ≤ w < 150.5
- B149 ≤ w < 151
- C149.5 ≤ w ≤ 150.5
- D150 ≤ w < 151
5.Calculate \frac{16.379 - 0.879}{4.2 \times 1.241} correct to 2 significant figures.
Medium- A3.0
- B2.9
- C3.1
- D2.95
6.An equilateral triangle has side length 12 cm, correct to the nearest centimetre. Find the lower bound of the perimeter of the triangle.
Medium- A34.5 cm
- B35 cm
- C34 cm
- D35.5 cm
7.The area of a square is 42.5 cm2, correct to the nearest 0.5 cm2. Calculate the lower bound of the length of the side of the square.
Medium- A6.5 cm
- B6.48 cm
- C6.52 cm
8.Serge walks 7.9 km, correct to the nearest 100 metres. The walk takes 133 minutes, correct to the nearest minute. Calculate the maximum possible average speed of Serge’s walk in km/h.
Hard- A3.6 km/h
- B3.58 km/h
- C3.59 km/h
- D3.57 km/h