Question

1. determining the mass of an object three times gave the following results: 9.2 g, 9.1 g, and 9.3 g. find the mean mass and the average deviation from the mean.
2. normal body temperature is 37.0 °c. what is the corresponding fahrenheit temperature?

98.6°f

1. what is the mass in kilograms of 680 ml of a substance that has a density of 0.930 g/ml?
2. an object has a mass of exactly 5 g on an analytical balance that has an accuracy of 0.1 mg. to how many significant figures should this mass be recorded?

Explanation:

Step1: Calculate mean mass

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the individual values and $n$ is the number of values. Here, $n = 3$, $x_1=9.2$, $x_2 = 9.1$, $x_3=9.3$. So, $\bar{x}=\frac{9.2 + 9.1+9.3}{3}=\frac{27.6}{3}=9.2$ g.

Step2: Calculate deviation for each value

Deviation $d_i=\vert x_i-\bar{x}\vert$. For $x_1 = 9.2$, $d_1=\vert9.2 - 9.2\vert=0$; for $x_2 = 9.1$, $d_2=\vert9.1 - 9.2\vert = 0.1$; for $x_3=9.3$, $d_3=\vert9.3 - 9.2\vert=0.1$.

Step3: Calculate average deviation

The formula for average deviation $AD=\frac{\sum_{i = 1}^{n}d_{i}}{n}$. So, $AD=\frac{0 + 0.1+0.1}{3}=\frac{0.2}{3}\approx0.07$ g.

The formula to convert Celsius to Fahrenheit is $F=\frac{9}{5}C + 32$. Given $C = 37.0$. Then $F=\frac{9}{5}\times37.0+32=66.6 + 32=98.6^{\circ}F$.

The formula for density is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. Rearranging for mass gives $m=
ho V$. Given $
ho = 0.930$ g/mL and $V = 680$ mL. So $m=0.930\times680 = 632.4$ g. To convert to kg, divide by 1000: $m=\frac{632.4}{1000}=0.6324$ kg.

The balance has an accuracy of 0.1 mg or $0.0001$ g. The mass is 5 g. Since the balance can measure to four - decimal places in grams (0.0001 g), the mass should be recorded as 5.0000 g, which has 5 significant figures.

Answer:

Mean mass: 9.2 g; Average deviation: 0.07 g