1.3 Measures and Accuracy

• What are the units used to measure length?

  meters, centimeters, inches, feet
• Match the term with its definition and example:

  Accuracy ↔️ How close a measurement is to the true value ||| A thermometer reading 25.1°C when the true temperature is 25°C

  Precision ↔️ How consistent measurements are with each other ||| Several thermometers consistently reading between 25.0°C and 25.1°C
• What does accuracy refer to in measurement?

  Closeness to the true value
• Precision refers to how close a measurement is to the true value.

  False
• Accurate measurements enable better decision-making, reliable scientific experiments, and improved engineering designs
• Match the term with its definition:

  Accuracy ↔️ Closeness to the true value

  Precision ↔️ Consistency of measurements
• What is a direct measurement in the context of measurement types?

  Observing a physical quantity
• Calculating the area of a rectangle by measuring its length and width is an example of indirect measurement.
• Calculating the volume of a cylinder using the formula V = πr²h is a derived measurement.
• What does precision indicate in measurements?

  Consistency of measurements
• Measurement error is the difference between the measured value and the true value.
• Estimating length involves comparing the object to a known reference length.
• Percentage error is a measure of the accuracy of a measurement.
• What does high accuracy in calculations lead to?

  Reliable and accurate conclusions
• What are measures in mathematics?

  Quantitative properties
• Units are the standard quantities used to express and compare measures
• What are the units for measuring length?

  meters, centimeters, inches, feet
• Match the measure with its common units:

  Length ↔️ meters, inches

  Mass ↔️ kilograms, ounces

  Time ↔️ seconds, hours

  Temperature ↔️ degrees Celsius, Fahrenheit
• Accuracy in measurement is important for reliable scientific experiments.
• What is the definition of accuracy in measurement?

  Closeness to the true value
• A thermometer reading 25.1°C when the true temperature is 25°C is an example of accuracy
• Measuring the length of a table with a ruler is an example of direct measurement.
• What is the difference between precision and accuracy in measurement?

  Consistency vs. closeness to true value
• Precision is about the consistency of measurements, while accuracy is about how close the measurements are to the true value
• Arrange the following units from smallest to largest for measuring time:

  1️⃣ seconds

  2️⃣ minutes

  3️⃣ hours

  4️⃣ days
• Accurate measurements improve engineering designs and decision-making.
• What is an example of indirect measurement?

  Calculating the area of a rectangle
• The volume of a cylinder is calculated using the formula $V =$$\pi r^{2} h$, which is an example of a derived measurement
• Direct Measurement involves observing and recording a physical quantity
• What formula is used to calculate the area of a rectangle in indirect measurement?

  $A =$$lw$
• The formula for calculating the volume of a cylinder in derived measurement is $V =$$\pi r^{2} h$
• Direct measurements are always feasible for all quantities

  False
• Match the measurement type with its definition and example:

  Direct Measurement ↔️ Observing and recording a physical quantity ||| Measuring the length of a table with a ruler

  Indirect Measurement ↔️ Calculating a quantity using other measured values ||| Calculating the area of a rectangle using $A =$$lw$

  Derived Measurement ↔️ Calculating a quantity using a formula ||| Calculating the volume of a cylinder using $V =$$\pi r^{2} h$
• What does precision measure in measurements?

  Consistency of results
• Accuracy measures how close a measurement is to the true or accepted value
• Accuracy and precision are the same concept in measurements

  False
• Match the term with its definition and example:

  Precision ↔️ How close multiple measurements are to each other ||| Measurements of a table's length are 101.1 cm, 101.0 cm, and 101.2 cm

  Accuracy ↔️ How close a measurement is to the true value ||| Measuring a table's length as 101.0 cm when its true length is 101.1 cm
• What is measurement error defined as?

  Difference between measured and true value
• Systematic error is consistent and predictable
• What causes random error in measurements?

  Fluctuations in experimental conditions