Approximation and estimation
10 flashcards to master Approximation and estimation
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Round 3.14159 to 3 decimal places.
Identify the 4th decimal place (5). Since 5 ≥ 5, round up the 3rd decimal place. Therefore, 3.14159 rounded to 3 decimal places is 3.142.
Round 0.006789 to 2 significant figures.
The first significant figure is 6. The second is 7. Since the next digit is 8 (≥ 5), round 7 up to 8. The answer is 0.0068.
Estimate the value of (4.8 × 10.1) / 2.3 by rounding each number to 1 significant figure.
Round 4.8 to 5, 10.1 to 10, and 2.3 to 2. The estimation is (5 × 10) / 2 = 25. Therefore, the estimated value is 25.
Define 'upper bound' in the context of approximation.
The upper bound is the largest possible value a quantity could be, given a certain level of accuracy or rounding. It represents the maximum limit of the true value.
A length is measured as 8.6 cm, correct to the nearest 0.1 cm. Find the upper bound of the length.
The upper bound is found by adding half of the degree of accuracy (0.1/2 = 0.05) to the measured value. Upper bound = 8.6 + 0.05 = 8.65 cm.
A length is measured as 8.6 cm, correct to the nearest 0.1 cm. Find the lower bound of the length.
The lower bound is found by subtracting half of the degree of accuracy (0.1/2 = 0.05) from the measured value. Lower bound = 8.6 - 0.05 = 8.55 cm.
Explain the difference between 'rounding' and 'truncation'.
Rounding adjusts a number to the nearest specified place value, while truncation simply cuts off the digits beyond a certain point without any adjustment.
The sides of a rectangle are measured as 6 cm and 4 cm, correct to the nearest cm. Calculate the upper bound of the area.
The upper bound of each side is 6.5 cm and 4.5 cm. The upper bound of the area is (6.5)(4.5) = 29.25 cm².
What does 'degree of accuracy' mean in the context of measurement?
Degree of accuracy refers to the smallest unit a measurement device can reliably distinguish. It determines the possible error range in the measurement.
Key Questions: Approximation and estimation
Define 'upper bound' in the context of approximation.
The upper bound is the largest possible value a quantity could be, given a certain level of accuracy or rounding. It represents the maximum limit of the true value.
What does 'degree of accuracy' mean in the context of measurement?
Degree of accuracy refers to the smallest unit a measurement device can reliably distinguish. It determines the possible error range in the measurement.
About Approximation and estimation (1.6)
These 10 flashcards cover everything you need to know about Approximation and estimation for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.
What You'll Learn
- 3 Definitions - Key terms and their precise meanings that examiners expect
- 1 Key Concepts - Core ideas and principles from the 0580 syllabus
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After mastering Approximation and estimation, explore these related topics:
- 1.5 Ratio, proportion and rate - 10 flashcards
- 1.7 Limits of accuracy - 9 flashcards
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