Chapter 1, Problem 69A

(a)

To determine

More precise number from the measurement.

Answer to Problem 69A

The speed measurement by the first scientist is more precise.

Explanation of Solution

Given Info:

The speed measurement by the first scientist is, $u=\left(3.001\pm 0.001\right)\times {10}^8\text{m}/\text{s}$ .

The speed measurement by the second scientist is, $v=\left(2.999\pm 0.006\right)\times {10}^8\text{m}/\text{s}$ .

Calculation:

The precision is the measure how close the measurement is to exact reading. The measurement of the speed by the first scientist is more precise because it can be measured up to $\pm 0.001$ . The speed measurement by the second scientist can only up to $\left(2.999\pm 0.006\right)$ .

Thus, the speed measurement by the first scientist is more precise.

(b)

To determine

The more accurate speed from the both measurements.

Answer to Problem 69A

The speed measurement of the second scientist is more accurate and the value of accurate measurement is $2.999\times {10}^8\text{m}/\text{s}$ .

Explanation of Solution

Calculation:

The accuracy is the closeness of the measurement with the standard value of the measurement. The standard value of the speed of the light is $3\times {10}^8\text{m}/\text{s}$ that is more close with the measured speed $2.999\times {10}^8\text{m}/\text{s}$ .

Thus, the speed measurement of the second scientist is more accurate and the value of accurate measurement is $2.999\times {10}^8\text{m}/\text{s}$ .