1.3 Measures and Accuracy

• An example unit for length is a meter
• The conversion factor for meters to centimeters is 100
• Match the concept with its description:

  Measuring ↔️ Precise determination using tools

  Estimating ↔️ Rough approximation without tools
• 1 meter equals 1000 centimeters

  False
• What is the conversion factor for kilograms to grams?

  1000
• Measuring requires tools like rulers and scales
• Measuring always provides a ballpark figure or range.

  False
• What do significant figures indicate about a measurement?

  Reliability
• Captive zeros between non-zero digits are always significant.


  True
• When adding 14.6 and 3.12, to how many decimal places should the result be rounded?

  One
• What is the first step in rounding a number to significant figures?

  Identify significant figures
• Rounding to decimal places is used when overall magnitude is more important than decimal accuracy.

  False
• Leading zeros in a number are never significant
• When performing calculations, the result should be rounded to the fewest significant figures
• In multiplication, the result should be rounded based on the fewest significant figures
• Conversion factors allow you to express a measurement in different units.


  True
• Measuring provides a precise numerical value, while estimating gives a ballpark figure.


  True
• Significant figures reflect the reliability of a measurement by showing how many digits are known with certainty.

  True
• Are leading zeros in a number significant?

  No
• The number of significant figures used depends on the context and required level of precision.


  True
• Order the steps for rounding to significant figures.

  1️⃣ Identify the significant figures

  2️⃣ Determine the required number of significant figures

  3️⃣ If the digit following the last significant figure is 5 or more, round up; otherwise, round down

  4️⃣ Replace remaining digits with zeros to maintain the number's magnitude
• Error bounds represent the range of values within which the true value is expected to lie.
• Match the concept with its definition.

  Error Bounds ↔️ Range of values where true value is expected

  Margin of Error ↔️ Maximum expected difference from true value
• When performing calculations, the final result should be rounded to the fewest significant figures present in any of the original values.

  True
• What are units of measurement used for?

  Measuring physical properties
• What is the purpose of converting between units?

  Ensuring consistency in calculations
• Estimating involves precise numerical values using standard units

  False
• When converting 5 meters to centimeters, you multiply by 100
• Match the concept with its characteristic:

  Measuring ↔️ Requires precision and tools

  Estimating ↔️ Rough approximation without precision
• Estimating involves a rough approximation of a quantity without precise measurement
• Measuring is quicker than estimating when precise values are not required.

  False
• Leading zeros are never significant
• Trailing zeros in a number without a decimal point are always significant.

  False
• Leading zeros are always significant.

  False
• Match the scenario with the rounded number to the correct number of significant figures:

  Length: 3.14159 rounded to 3 significant figures ↔️ 3.14

  Mass: 12345.6 rounded to 4 significant figures ↔️ 12350

  Time: 0.02789 rounded to 2 significant figures ↔️ 0.028
• Non-zero digits are always significant.


  True
• Trailing zeros in a number with a decimal point are always significant
• In addition, the result should be rounded based on the fewest decimal places
• Units of measurement are standard quantities used to measure different physical properties
• Steps to convert between units

  1️⃣ Identify the units you want to convert from and to

  2️⃣ Find the conversion factor

  3️⃣ Multiply or divide the original value by the conversion factor