Q: Convert $0.000345$ meters to scientific notation and express it with the correct number of significant figures.

$3.45 \times 10^{-4}\ \mathrm{m}$

Q: A student needs to convert $5.00\ \mathrm{km}$ to centimeters. What is the correct answer, using the appropriate number of significant figures?

$5.00 \times 10^{5}\ \mathrm{cm}$

Question 1

Which of the following best describes the purpose of using significant figures in scientific measurements?

Accepted Answer

To indicate the precision of a measurement and reflect the uncertainty in the last digit.

Question 2

A student measures the mass of a sample as $12.30\ \mathrm{g}$ and its volume as $4.56\ \mathrm{mL}$. What is the density of the sample, reported with the correct number of significant figures?

Accepted Answer

$2.7\ \mathrm{g/mL}$

Question 3

Which of the following numbers contains the correct number of significant figures for the result of the calculation $0.00456 	imes 2.1$?

Accepted Answer

$0.0096$

Question 4

Convert $0.000345$ meters to scientific notation and express it with the correct number of significant figures.

Accepted Answer

$3.45 	imes 10^{-4}\ \mathrm{m}$

Question 5

A chemist records the temperature of a reaction as $25.0\ ^\circ\mathrm{C}$. What is this temperature in Kelvin?

Accepted Answer

$298.0\ \mathrm{K}$

Question 6

Which of the following statements about accuracy and precision is correct?

Accepted Answer

Accuracy refers to how close measurements are to the true value, while precision refers to how close measurements are to each other.

Question 7

A student needs to convert $5.00\ \mathrm{km}$ to centimeters. What is the correct answer, using the appropriate number of significant figures?

Accepted Answer

$5.00 	imes 10^{5}\ \mathrm{cm}$

Question 8

Which of the following best explains why a measurement of $2.00\ \mathrm{g}$ is considered more precise than a measurement of $2\ \mathrm{g}$?

Accepted Answer

Because $2.00\ \mathrm{g}$ has more significant figures, indicating a smaller uncertainty.

Question 9

A laboratory scale gives a mass reading of $0.0560\ \mathrm{kg}$. How many significant figures are in this measurement?

Accepted Answer

4

Question 10

A student measures the length of a metal rod as $12.45\ \mathrm{cm}$ and $12.47\ \mathrm{cm}$ in two separate trials. What is the average length, reported with the correct number of significant figures?

Accepted Answer

$12.46\ \mathrm{cm}$

Question 11

Which of the following is the correct conversion factor to use when converting from milliliters to liters?

Accepted Answer

$1\ \mathrm{L} = 1000\ \mathrm{mL}$

Question 12

A block of wood has a mass of $150.0\ \mathrm{g}$ and a volume of $200.0\ \mathrm{cm}^3$. Will the block float or sink in water? (Density of water is $1.00\ \mathrm{g/cm}^3$)

Accepted Answer

It will float because its density is less than that of water.

Question 13

Which of the following best describes the difference between random and systematic errors in measurements?

Accepted Answer

Random errors are unpredictable and vary in magnitude and direction, while systematic errors are consistent and repeatable.

Question 14

A solution is prepared by mixing $25.0\ \mathrm{mL}$ of ethanol (density $0.789\ \mathrm{g/mL}$) with $40.0\ \mathrm{mL}$ of water (density $1.00\ \mathrm{g/mL}$). What is the total mass of the solution, reported with the correct number of significant figures?

Accepted Answer

$59.8\ \mathrm{g}$

Question 15

Which of the following is the correct way to express $0.000560$ in scientific notation with the correct number of significant figures?

Accepted Answer

$5.60 	imes 10^{-4}$

Question 16

A measurement is recorded as $3.40 	imes 10^2\ \mathrm{m}$. How many significant figures does this value have?

Accepted Answer

3

Question 17

A nurse needs to administer a medication at a dose of $0.250\ \mathrm{mg}$ per kilogram of body weight. If a patient weighs $70.0\ \mathrm{kg}$, how many milligrams of medication should be given, using the correct number of significant figures?

Accepted Answer

$17.5\ \mathrm{mg}$

Question 18

Which of the following is the correct order of steps when solving a unit conversion problem?

Accepted Answer

Identify the given quantity, write the conversion factor, set up the calculation, perform the calculation, check significant figures.

Question 19

A student records the following measurements: $2.34\ \mathrm{g}$, $2.36\ \mathrm{g}$, and $2.35\ \mathrm{g}$. The true mass is $2.50\ \mathrm{g}$. Which statement best describes the accuracy and precision of these measurements?

Accepted Answer

The measurements are precise but not accurate.

Essentials: Units, Measurement, & Problem Solving – Study Notes

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