Learning Objectives:

• Define accuracy.
• Differentiate between precision and accuracy.
• Distinguish exact and uncertain numbers.

Accuracy:

Accuracy: How closely a measurement aligns with a correct value.

Precision:

• Exact number: Number derived by counting or by definition.
  

• Precision: How closely a measurement matches the same measurement when repeated.

Solved Example: 1-10-01

Consider the following statements for dynamic characteristics of a measurement system:

1. Fidelity is defined as the degree to which a measurement system indicates changes in the measured quantity without any dynamic error.

2. Dynamic error is the difference between the true value of the quantity changing with time and the value indicated by the measurement system if no static error is assumed.

3. Measuring lag is the retardation in the response of a measurement system to changes in the measured quantity.

Which of the above statements are correct?

A. 1 and 2 only

B. 1 and 3 only

C. 1, 2 and 3

D. 2 and 3 only

Correct Answer: D

Solved Example: 1-10-02

Trueness from the reference measures:

A. Precision

B. Mean

C. Accuracy

D. Recall

Correct Answer: C

Solved Example: 1-10-03

Which one of the following has the highest accuracy?

A. Standard resistance

B. Standard inductance

C. Standard capacitance

D. Standard mutual inductance

Correct Answer: A

Solved Example: 1-10-04

The property of a measuring instrument to give the output very close to the actual value is termed as:

A. Sensitivity

B. Repeatability

C. Precision

D. Accuracy

Correct Answer: D

Solved Example: 1-10-05

Consider the following statements for accuracy of the instrument:

1. The accuracy of the instrument may be specified in terms of limits of error.

2. The specification of a point accuracy gives any information about the general accuracy of the instrument.

3. The best way to conceive the idea of accuracy is to specify it in terms of the true value of the quantity being measured.

Which of the above statements are correct?

A. 1 and 2 only

B. 1 and 3 only

C. 1, 2 and 3

D. 2 and 3 only

Correct Answer: B

Solved Example: 1-10-06

Which one of the following statement is not correct?

A. It is not possible to have precise measurements which are not accurate.

B. Correctness in measurement requires both accuracy and precision

C. Reproducibility and consistency are expressions that best describe precision in measurements

D. An instrument with 2% accuracy is better than another with 5% accuracy

Correct Answer: A

Learning Objectives:

• Correctly represent uncertainty in quantities using significant figures.
• Apply proper rounding rules to computed quantities.

• Rounding: Procedure used to ensure that calculated results properly reflect the uncertainty in the measurements used in the calculation.

• Significant figures: (also, significant digits) all of the measured digits in a determination, including the uncertain last digit.

• Uncertainty: Estimate of amount by which measurement differs from true value.

Every measurement has some uncertainty, which depends on the device used (and the user’s ability). All of the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits.

The three rules for rounding numbers:

1. When we add or subtract numbers, we should round the result to the same number of decimal places as the number with the least number of decimal places (the least precise value in terms of addition and subtraction).

2. When we multiply or divide numbers, we should round the result to the same number of digits as the number with the least number of significant figures (the least precise value in terms of multiplication and division).

3. If the digit to be dropped (the one immediately to the right of the digit to be retained) is less than 5, we “round down” and leave the retained digit unchanged; if it is more than 5, we “round up” and increase the retained digit by 1; if the dropped digit is 5, we round up or down, whichever yields an even value for the retained digit. (The last part of this rule may strike you as a bit odd, but it’s based on reliable statistics and is aimed at avoiding any bias when dropping the digit “5,” since it is equally close to both possible values of the retained digit.)

Solved Example: 1-15-01

Which one of the following has a terminating decimal expansion?

A. $\dfrac{1}{6}$

B. $\dfrac{17}{25}$

C. $\dfrac{10}{3}$

D. $\dfrac{1}{11}$

\begin{align*} \dfrac{1}{6} &= 0.16666666.......\\ \dfrac{17}{25} &= 0.68\\ \dfrac{10}{3} &= 3.3333333.....\\ \dfrac{1}{11} &= 0.11111....... \end{align*}

Correct Answer: B