1.3 Measures and Accuracy

• **Decimal places** refer to the number of digits that appear after the decimal point in a number.


  True
• **Significant figures** indicate the precision of a measurement, while **decimal places** indicate the position of the decimal
• Steps to round a measurement to significant figures:

  1️⃣ Identify the required number of significant figures

  2️⃣ Count from the first non-zero digit

  3️⃣ Examine the digit to the right

  4️⃣ Round up if 5 or greater
• Why is it important to use the correct number of significant figures?

  Avoid over-precision
• When rounding to significant figures, round down if the next digit is 4 or less.


  True
• Rounding to decimal places reduces the number of digits after the decimal point.


  True
• What is involved in rounding measurements to decimal places?

  Reducing digits after decimal
• What is 3.14159 rounded to 2 decimal places?

  3.14
• What does an error interval represent in measurements?

  True value range
• What is the absolute error in a measurement if the measured value is 12.5 cm and the true value is 12.0 cm?

  0.5 cm
• Leading zeros are not counted as significant figures but are included in counting the number of decimal places
• Steps for rounding measurements to significant figures

  1️⃣ Identify the required number of significant figures

  2️⃣ Count from the first non-zero digit

  3️⃣ Examine the digit to the right of the last significant figure

  4️⃣ Round up if the digit is 5 or greater

  5️⃣ Drop any remaining digits
• Leading zeros are counted as significant figures.

  False
• 0.002567 rounded to 2 significant figures is 0.0026
• Match the concept with its definition:

  Tolerance ↔️ Acceptable range of values

  Error Interval ↔️ Range containing true value
• A percentage error of 4.17% indicates the measurement has good accuracy.


  True
• Percentage error measures how accurate a measurement is compared to the true value.


  True
• What do significant figures indicate about a measurement?

  Precision
• A number with 0.0045 has 2 significant figures.


  True
• When rounding 12345 to 3 significant figures, the rounded result is 12300
• What does the number of decimal places in a measurement indicate?

  Position of decimal point
• When rounding 4.567 to 3 significant figures, the rounded result is 4.57
• Steps to round a measurement to decimal places:

  1️⃣ Identify the decimal place to round to

  2️⃣ Examine the digit immediately to the right

  3️⃣ Round up if 5 or greater

  4️⃣ Keep as is if less than 5
• The first step in rounding measurements to decimal places is to identify the decimal place to round to
• A tolerance in measurements refers to the acceptable range of values
• The formula for calculating percentage error is: $Percentage\ error =$$\frac{Absolute\ error}{True\ value} \times 100$, where the true value is the denominator and 100 is used to express the result as a percentage
• A percentage error of 4.17% indicates that the measured value is approximately 4% different from the true value.


  True
• What is the first step in rounding a measurement to significant figures?

  Identify significant figures
• What is 12345 rounded to 3 significant figures?

  12300
• 0.002567 rounded to 2 significant figures is 0.0026
• When rounding to decimal places, if the next digit is 5 or greater, you round up the last decimal place digit.

  True
• A tolerance of 10 cm ± 0.5 cm means acceptable measurements range from 9.5 cm to 10.5
• Match the term with its meaning:

  Significant Figures ↔️ Precision of measurement

  Decimal Places ↔️ Position of decimal point
• Significant figures refer to the meaningful digits in a number, including the first non-zero digit
• Which digits are included when counting significant figures?

  All non-zero digits
• A number with 0.0045 has 4 decimal places.


  True
• When rounding 0.002567 to 2 significant figures, the rounded result is 0.0026
• Significant figures include leading zeros in a number.

  False
• When rounding 0.00456 to 2 significant figures, the rounded result is 0.0046
• When rounding 3.14159 to 2 decimal places, the rounded result is 3.14