Chapter 5, Problem 1P

Determine the precision, accuracy, and greatest possible error of measurement numbers.

Determine the precision of each of the following measurement numbers. Which one is most precise?

1. (a) 4.27 psi
2. (b) 6758 psi
3. (c) 350 psi
4. (a) _______________
5. (b) _______________
6. (c) _______________

Determine the number of significant digits in each of the following measurement numbers.

1. (d) 9.6 kg
2. (e) 458 kg
3. (f) 6000 kg
4. (d) _______________
5. (e) _______________
6. (f) _______________

Determine the greatest possible error of each measurement.

1. (g) 450 psi
2. (h) 8.6 kg
3. (i) $3\frac{1}{4}$ in.
4. (g) _______________
5. (h) _______________
6. (i) _______________

To determine

To state: The precision of the measurement 4.27 psi.

Answer to Problem 1P

The measurement 4.27 psi is precise to the nearest hundredth psi.

Explanation of Solution

Definition used:

Precision:

“The precision of a measurement number is indicated by the place value of its right-most significant digit”.

Description:

The given measurement number is 4.27 psi.

The precision of the measurement 4.27 psi can be obtained as follows.

$\begin{array}{l}4.\underset{\downarrow }{27}\text{ psi}\\ \text{To the nearest hundredth of psi}\end{array}$

Thus, the measurement 4.27 psi is precise to the nearest hundredth psi.

To determine

To state: The precision of the measurement 6758 psi.

Answer to Problem 1P

The measurement 6758 psi is precise to the nearest one psi.

Explanation of Solution

The given measurement number is 6758 psi.

The precision of the measurement 6758 psi can be obtained as follows.

$\begin{array}{l}\underset{\downarrow }{6758}\text{ psi}\\ \text{To the nearest one pound}\end{array}$

Thus, the measurement 6758 psi is precise to the nearest one psi.

To determine

To state: The precision of the measurement 350 psi.

Answer to Problem 1P

The measurement 350 psi is precise to the nearest ten psi.

Explanation of Solution

The given measurement number is 350 psi.

The precision of the measurement 350 psi can be obtained as follows.

$\begin{array}{l}\underset{\downarrow }{\text{360 }}\text{ psi}\\ \text{To the nearest ten volts}\left(\because \text{The last zero is not significant}\right)\end{array}$

Thus, the measurement 350 psi is precise to the nearest ten psi.

To determine

To identify: The most precision of the measurement from part (a) through part (c).

Answer to Problem 1P

The most precision of the measurement is 4.27 psi.

Explanation of Solution

Definition used:

From part (a) through part (b), the precision of the measurements 4.27 psi, 6758 psi, and 360 psi are hundredth psi, one psi, and ten psi, respectively.

In order to identify the most precision of the measurements, first check the right most significant digits of 4.27 psi, 6758 psi, and 360 psi.

Here, the measurement of 4.27 psi is precise to nearest hundredth psi which is right most significant after decimal compare to others.

Thus, the most precision of the measurement is 4.27 psi.

To determine

The accuracy of the measurement 9.6 kg.

Answer to Problem 1P

The number 9.6 kg is accurate to two significant digits.

Explanation of Solution

Definition used:

Accuracy:

“The accuracy of a measurement number refers to the number of significant digit that it contains”.

Description:

The given measurement number is 9.6 kg.

Note that, the number of digit in the number 9.6 kg is two.

Thus, by the above definition the number 9.6 kg can be accurate to two significant digits.

To determine

The accuracy of the measurement 458 kg.

Answer to Problem 1P

The number 458 kg is accurate to three significant digits.

Explanation of Solution

The given measurement number is 458 kg.

Note that, the number of digit in the number 458 kg is three.

Thus, by the above definition the number 458 kg can be accurate to three significant digits.

To determine

The accuracy of the measurement 350 kg.

Answer to Problem 1P

The number 350 kg is accurate to two significant digits.

Explanation of Solution

The given measurement number is 350 kg.

Note that, the zeros are not significant.

That is, the number of digit in the number 350 kg is two.

Thus, by the above definition the number 350 kg can be accurate to two significant digits.

To determine

The greatest possible error in the number 450 psi.

Answer to Problem 1P

The greatest possible error in the number 450 psi is 0.05.

Explanation of Solution

Definition used:

Greatest possible error:

“The greatest possible error of a measurement is defined as half the precision of that measurement”.

Description:

The given measurement number is 450 psi.

By the part (c) method, it is observed that the measurement number 450 psi is precise to the nearest tenth, that is, 0.1.

Note that, half of the precision number 0.1 is 0.05.

Thus, by the above definition the greatest possible error in the number 450 psi is 0.05.

To determine

The greatest possible error in the number 8.6 kg.

Answer to Problem 1P

The greatest possible error in the number 8.6 kg is 0.05.

Explanation of Solution

The given measurement number is 8.6 kg.

By the part (a) method, it is observed that the measurement number 8.6 kg is precise to the nearest tenth, that is, 0.1.

Note that, half of the precision number 0.1 is 0.05.

Thus, by the above definition the greatest possible error in the number 8.6 kg is 0.05.

To determine

The greatest possible error in the number $3\frac{1}{4}\text{ in}\text{.}$.

Answer to Problem 1P

The greatest possible error in the number $3\frac{1}{4}\text{ in}\text{.}$ is $\underset{\_}{\frac{1}{8}\text{ in}}.$.

Explanation of Solution

The given measurement number is $3\frac{1}{4}\text{ in}\text{.}$.

The precision of the measurement number $3\frac{1}{4}\text{ in}\text{.}$ is $\frac{1}{4}$.

Note that, half of the precision number $\frac{1}{4}$ is $\frac{1}{8}$.

Thus, by the above definition the greatest possible error in the number $5\frac{1}{4}\text{ in}\text{.}$ is $\underset{\_}{\frac{1}{8}\text{ in}}.$.