1.3.4 Estimating results, evaluating accuracy of measurement

• When rounding to the nearest ten, a units digit of 5 or more requires rounding up.

  True
• What are significant figures used for in measurements?

  Precision of measurements
• The absolute value of the difference between the measured and true values is always positive.

  True
• Arrange the rounding categories from smallest to largest place value:

  1️⃣ Nearest Whole Number

  2️⃣ Nearest Ten

  3️⃣ Nearest Hundred
• Leading zeros are significant in a number.

  False
• Estimating the cost of 3 pizzas at £12.75 each results in an estimated cost of £39.

  True
• What are the three main types of errors in measurements?

  Gross, systematic, random
• If you notice a consistent bias in your measurements, which type of error is most likely the cause?

  Systematic Error
• What is the percentage error if a length is measured as 26 cm when the true value is 25 cm?

  4%
• Match the step with its description:

  Calculate the absolute difference ↔️ |Measured - True| = |26 - 25| = 1

  Divide by the true value ↔️ 1 / 25 = 0.04

  Multiply by 100% ↔️ 0.04 x 100% = 4%
• Are zeros between significant digits considered significant?

  Yes
• Reliability refers to the consistency of a measurement, while validity refers to its accuracy.

  True
• What is the "Loading Effect" error?

  An error caused by the measurement instrument affecting the quantity being measured.
• What is the difference between Systematic Error and Random Error?

  Systematic Error is consistent and predictable, while Random Error is unpredictable and varies
• Match the error type with its cause:

  Gross Errors ↔️ Human mistakes, calculation errors

  Systematic Errors ↔️ Consistent measurement problems

  Random Errors ↔️ Unpredictable variations
• What are the three main types of errors related to the instrument?

  • Instrumental Error
  • Misuse of Instruments
  • Inherent shortcomings of Instruments
• What is the rule for trailing zeros in numbers with decimal points?

  They are significant
• Match the error type with its effect:

  Gross Errors ↔️ Dramatic outliers

  Systematic Errors ↔️ All measurements off by same amount

  Random Errors ↔️ Measurements scatter around true value
• Systematic errors can be caused by instrumental, environmental, or observational issues.

  True
• Validity addresses whether the measurement is truly measuring what it should.


  True
• When rounding to the nearest whole number, a decimal of 0.5 or more requires rounding up.

  True
• In calculating the area of a circle, what value of π gives a more accurate result?

  3.14159
• How do Observational Errors differ from other types of errors shown?

  Observational Errors are caused by the observer, unlike Instrumental, Environmental, and Random Errors
• What is the formula for calculating percentage error?

  $(|Measured Value - True Value| / True Value) x 100$
• Random errors are caused by predictable variations in measurements.

  False
• When rounding to the nearest hundred, tens and units digits of 50 or more require rounding up.


  True
• Lower percentage error indicates more accurate measurements.


  True
• What is the difference between Instrumental Error and Environmental Error?

  Instrumental Error is caused by the instrument itself, while Environmental Error is caused by external factors in the environment.
• What impact does high accuracy have on decision-making?

  Sound decisions
• When are trailing zeros significant?

  With decimal points
• Low accuracy in scientific measurements can lead to incorrect conclusions.


  True
• Gross errors result in dramatic outliers in measurements.

  True
• High accuracy leads to approximate and less reliable results.

  False
• Why is knowing significant figures important in calculations?

  For accurate results
• Steps to calculate percentage error

  1️⃣ Find the absolute difference between the measured and true values

  2️⃣ Divide the absolute difference by the true value

  3️⃣ Multiply the result by 100%
• Zeros before the first non-zero digit are not significant.

  True
• Match the term with its definition:

  Reliability ↔️ Consistency of a measurement

  Validity ↔️ Accuracy of a measurement
• What does accuracy measure in calculations?

  Closeness to true value
• Estimating can help you check if your final answer is reasonable.


  True
• Minimizing percentage errors is crucial for achieving high accuracy.


  True