Question

1. match the item with the best unit for its measurement.

a. coin’s width

1. km

b. marathon

1. cm

c. building

1. mm

d. book

1. m
2. three different groups of students performed the same density lab measurements. each group completed two trials for the substance being tested. actual mass = 12.06 g and actual volume = 1.12 ml.

group	trial	mass (g)	volume (ml)
#1	2	12.12	1.15
#2	1	11.03	2.13
#2	2	10.98	1.99
#3	1	14.95	17.23
#3	2	17.63	19.87

a) which group has good precision, but poor accuracy? explain.
b) which group is neither accurate nor precise? explain.
c) which group had a set of results with the best combination of precision and accuracy? explain.
d) would the substance being tested by the students float in room temp. water? explain.

1. a sample of a metal is found to have a density of 15.4g/cm3 and a mass of 2.593g, what is the sample’s volume? show all work, including units and proper use of sig figs.

Explanation:

Question 13

Match each item to the most appropriate unit based on typical size/scale:

• A coin's width is very small, so millimeters (mm) fit best.
• A marathon is a long-distance race, measured in kilometers (km).
• A building is tall, so meters (M, m) are the right unit.
• A book's width is moderate, so centimeters (cm) work best.

First, define key terms:

• Accuracy: How close measurements are to the actual value.
• Precision: How close repeated measurements are to each other.

Actual values: Mass = 12.06 g, Volume = 1.12 mL

Part a

Group 2's two trials have very close mass (11.03 g / 10.98 g) and volume (2.13 mL / 1.99 mL) values (good precision), but both are far from the actual mass and volume (poor accuracy).

Part b

Group 3's two trials have very different mass (14.95 g / 17.63 g) and volume (17.23 mL / 19.87 mL) values (poor precision), and both are far from the actual values (poor accuracy).

Part c

Group 1's two trials have mass (12.00 g / 12.12 g) and volume (1.10 mL / 1.15 mL) values that are close to each other (good precision) and close to the actual mass and volume (good accuracy).

Part d

First calculate the actual density of the substance using $
ho = \frac{m}{V}$. Room temperature water has a density of ~1.0 g/mL. Substances with density greater than 1.0 g/mL sink, while those less float.

Step1: Recall density formula

Density $
ho = \frac{m}{V}$, rearrange to solve for volume: $V = \frac{m}{
ho}$

Step2: Substitute given values

$m = 2.593\ \text{g}$, $
ho = 15.4\ \text{g/cm}^3$
$V = \frac{2.593\ \text{g}}{15.4\ \text{g/cm}^3}$

Step3: Calculate and apply sig figs

The density has 3 significant figures, which is the least number of sig figs in the given values. Round the result to 3 sig figs.
$V \approx 0.168\ \text{cm}^3$

Answer:

a. 3. mm
b. 1. km
c. 4. M
d. 2. cm

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Question 14