1.5 Uncertainty in Measurement: Accuracy, Precision and Significant Figures

Every chemistry measurement has uncertainty, and mastering how to express it correctly is the difference between losing and gaining marks on AP, A-Level, IB, and college exams. This complete guide breaks down exact vs. inexact numbers, precision vs. accuracy, significant figure rules, and sig figs in calculations with worked examples, exam traps, and 3D visual diagrams so you can master measurement without ever opening the textbook.

Key Insights

• Measured numbers are always inexact while defined and counted numbers are exact with infinite significant figures.
• Precision measures how close repeated measurements agree, accuracy measures how close they are to the true value.
• All nonzero digits and specific zeros are significant, with distinct rules for leading, captive, and trailing zeros.
• Addition and subtraction are limited by fewest decimal places, while multiplication and division are limited by fewest significant figures.
• The final calculated answer should contain only one uncertain digit and requires proper rounding.

Uncertainty in Measurement

Every number you encounter in chemistry falls into one of two categories. Understanding this classification is the foundation for all exam calculations.

Exact numbers are those whose values are known exactly. There are two types:

1. Defined numbers: These are part of a definition. There are exactly 12 eggs in a dozen, exactly 1000 g in 1 kg, and exactly 2.54 cm in 1 inch. The number 1 in any conversion factor such as 1 m = 100 cm or 1 kg = 2.2046 lb is also exact. These numbers have an infinite number of significant figures.
2. Counted numbers: These result from counting discrete objects. If you count 7 beakers on a bench or 26 students in a classroom, that 7 and that 26 are exact.

Inexact numbers are those obtained by any measurement process. No measuring device is perfect. Every balance, ruler, graduated cylinder, and thermometer has inherent limitations, called equipment errors. In addition, different people read instruments slightly differently, introducing human errors.

Imagine ten students using ten different balances to determine the mass of the same dime. Even if they are careful, the ten values will vary slightly. Some balances may be calibrated differently, and each student may estimate the last digit differently. The core lesson: Uncertainties always exist in measured quantities. In scientific work we acknowledge this uncertainty in how we write the number itself.

Callout Box: Why We Never Write a Perfect MeasurementIn a lab report or exam, writing a measured mass as just "2.2 g" is not wrong, but it is incomplete without understanding its uncertainty. Professional chemists understand that this implies 2.2 ± 0.1 g. Your ability to interpret that hidden uncertainty is what AP and A-Level examiners test when they ask about significant figures.

Precision and Accuracy

These two words are used interchangeably in daily life, but in chemistry they have precise and different meanings that are tested constantly.

Precision is a measure of how closely individual measurements agree with one another. High precision means repeated trials give nearly identical values, regardless of whether those values are correct.

Accuracy refers to how closely individual measurements agree with the correct, or true, value. High accuracy means the average of your measurements is close to the true value.

Three photorealistic 3D dartboards side-by-side showing precision vs accuracy concepts with realistic darts

The dartboard analogy is the standard way to visualize this:

• Good accuracy, Good precision: All darts are tightly clustered in the bullseye. Your measurements are both reproducible and correct.
• Poor accuracy, Good precision: All darts are tightly clustered together, but far from the bullseye. This often happens when an instrument is poorly calibrated. A very sensitive balance that is not zeroed correctly will give masses that are consistently high or low. They are precise but inaccurate.
• Poor accuracy, Poor precision: Darts are scattered randomly across the board. This reflects both large random errors and a systematic error.

In the laboratory we rarely take just one measurement. We perform several trials and average the results. The precision of those measurements is often expressed in terms of the standard deviation, which reflects how much the individual measurements differ from the average. A small standard deviation means high precision and gives us confidence that our procedure is reproducible. However, a small standard deviation does not guarantee accuracy.

Feature	Precision	Accuracy
Definition	Closeness of measurements to each other	Closeness of measurements to true value
Reflects	Reproducibility, random error	Correctness, systematic error
Can be improved by	More careful technique, better reproducibility	Calibration, better standards
High precision but low accuracy is possible?	Yes, very common	No, this requires both

Pro Tip for Exams:If a question asks "Why are the results precise but not accurate?" the answer is almost always "systematic error / poor calibration" or "consistent instrumental error." If it asks why results are neither precise nor accurate, mention random errors.

Exam Trap:Students think precise measurements must be accurate. They are not. AP Chemistry loves to give you a data set where all trials are 10.5, 10.6, 10.5 g when the true value is 9.0 g and asks you to describe it. Answer: Precise but inaccurate.

Significant Figures

How do we communicate the uncertainty of a measurement without writing ± every time? Through significant figures.

Suppose you determine the mass of a dime on a balance capable of measuring to the nearest 0.0001 g. You could report the mass as 2.2405 ± 0.0001 g. The ± notation expresses the magnitude of the uncertainty. In most scientific work we drop the ± notation with the understanding that there is always some uncertainty in the last digit reported for any measured quantity.

Consider a liquid-in-glass thermometer. The liquid column lies between the 25 °C and 30 °C scale marks. We can read the certain digits from the scale marks and must estimate the uncertain one. We see it is between 25 and 30, but a little more than halfway, so we estimate 27 °C. The second digit is our estimated, uncertain digit.

Photorealistic 3D laboratory thermometer with magnified inset showing estimated digit and digital analytical balance displaying 2.2405g

All digits of a measured quantity, including the uncertain one, are called significant figures. A measured mass reported as 2.2 g has two significant figures, while one reported as 2.2405 g has five significant figures. The greater the number of significant figures, the greater the certainty implied for the measurement.

The difference between 4.0 g and 4.00 g is a classic exam point. The value 4.0 has two significant figures. This implies the uncertainty is in the first decimal place. We understand it to mean 4.0 ± 0.1 g, so the true mass could be anywhere from 3.9 to 4.1 g. The value 4.00 has three significant figures. This implies the uncertainty is in the second decimal place, meaning 4.00 ± 0.01 g, or 3.99 to 4.01 g. Without further information, we cannot be sure whether that difference in uncertainty reflects precision or accuracy, but we know 4.00 is a more precise statement.

If a sample has a mass of about 25 g and is placed on a balance that has a precision of ±0.001 g, you should report five significant figures. For example, 24.995 g, where the uncertainty is in the third decimal place.

To determine the number of significant figures in a reported measurement, read the number from left to right, counting digits starting with the first digit that is not zero. In any measurement that is properly reported, all nonzero digits are significant.

Zeros are tricky because they can be part of the measured value or merely locate the decimal point:

1. Zeros between nonzero digits are always significant. 1005 kg has four significant figures. 7.03 cm has three significant figures.
2. Zeros at the beginning of a number are never significant; they merely indicate the position of the decimal point. 0.02 g has one significant figure. 0.0026 cm has two significant figures.
3. Zeros at the end of a number are significant if the number contains a decimal point. 0.0200 g has three significant figures. 3.0 cm has two significant figures.

A problem arises when a number ends with zeros but contains no decimal point. In such cases, it is normally assumed that the zeros are not significant. Exponential notation can be used to clearly indicate whether end zeros are significant. For example, a mass of 10,300 g can be written to show three, four, or five significant figures:

• 1.03 × 10⁴ g (three significant figures)
• 1.030 × 10⁴ g (four significant figures)
• 1.0300 × 10⁴ g (five significant figures)

In these numbers all zeros to the right of the decimal point are significant. The exponential term 10⁴ does not add to the number of significant figures.

Photorealistic 3D white numbers showing significant figure zero rules with gold highlights

Example	Sig Figs	Reason
4.003	Four	Zeros between nonzero digits are significant
6.023 × 1023	Four	Exponential term does not count
5000	One	No decimal point, trailing zeros assumed not significant
5000.	Four	Decimal point shows zeros are significant
5.00 × 103	Three	Zeros after decimal in coefficient are significant
3.549 g	Four	All nonzero digits
2.3 × 104 cm	Two	Only 2 and 3 count
0.00134 m3	Three	Leading zeros never count

Callout Box: The Atlantic-Pacific Rule for Quick CountingFor fast exams: If decimal point is Present, count from Pacific side (left, starting from first non-zero). If decimal point is Absent, count from Atlantic side (right). It helps you avoid missing leading vs trailing zeros under pressure.

Pro Tip for Exams: In AP and IB, always convert ambiguous numbers like 5000 into scientific notation if you want to show significance. Writing 5.00 × 10^3 explicitly tells the examiner you mean three significant figures.

Exam Trap:Students count leading zeros as significant. 0.0026 cm is NOT four significant figures, it is two. The zeros are only placeholders. Similarly, students think 5000 automatically has four sig figs. Without a decimal point, it has one by convention.

Significant Figures in Calculations

When you carry measured quantities through calculations, the least certain measurement limits the certainty of the calculated quantity and thereby determines the number of significant figures in the final answer. The final answer should be reported with only one uncertain digit.

There are two different rules, one for addition and subtraction, and another for multiplication and division.

01. For addition and subtraction, the result has the same number of decimal places as the measurement with the fewest decimal places. When the result contains more than the correct number of significant figures, it must be rounded off.

Example:

• 20.42 (two decimal places) ← this number limits the result
• 1.322 (three decimal places)
• 83.1 (one decimal place)

Sum = 20.42 + 1.322 + 83.1 = 104.842

We report the result as 104.8 because 83.1 has only one decimal place.

02. For multiplication and division, the result contains the same number of significant figures as the measurement with the fewest significant figures. When the result contains more than the correct number of significant figures, it must be rounded off.

Example: The area of a rectangle whose measured edge lengths are 6.221 cm and 5.2 cm should be reported as 32 cm² even though a calculator shows 32.3492 cm².

Area = (6.221 cm)(5.2 cm) = 32.3492 cm² → round off to 32 cm² because 5.2 has two significant figures.

Notice the critical difference: for addition and subtraction, decimal places are counted, whereas for multiplication and division, significant figures are counted.

In determining the final answer for a calculated quantity, exact numbers are assumed to have an infinite number of significant figures. Thus, when we say "There are 12 inches in 1 foot," the number 12 is exact, and we need not worry about the number of significant figures in it.

Photorealistic 3D comparison of addition vs multiplication significant figure rules with beakers and box

Rounding Rules:

In rounding off numbers, look at the leftmost digit to be removed:

• If the leftmost digit removed is less than 5, the preceding number is left unchanged. Rounding 7.248 to two significant figures gives 7.2.
• If the leftmost digit removed is 5 or greater, the preceding number is increased by 1. Rounding 4.735 to three significant figures gives 4.74, and rounding 2.376 to two significant figures gives 2.4.

Callout Box: The Special Case of Exactly 5Your instructor may want you to use a slight variation when the leftmost digit to be removed is exactly 5 with no following digits or only zeros. One common practice, called round-to-even, is to round up to the next higher number if that number will be even and down to the next lower number otherwise. Thus, 4.7350 would be rounded to 4.74, and 4.7450 would also be rounded to 4.74. This reduces bias in large data sets. For AP and A-Level, the simple "5 or greater round up" rule is usually accepted unless your syllabus states otherwise.

Worked Examples from The Central Science:

Volume of a box: The width, length, and height of a small box are 15.5 cm, 27.3 cm, and 5.4 cm, respectively. Calculate the volume using the correct number of significant figures.

Solution: Volume = width × length × height = (15.5 cm)(27.3 cm)(5.4 cm) = 2285.01 cm³. We can show only as many significant figures as given in the dimension with the fewest significant figures, that for the height (two significant figures). Because the resulting number is 2300, it is best reported in exponential notation, 2.3 × 10³ cm³, to clearly indicate two significant figures.

Average speed: It takes 10.5 s for a sprinter to run 100.00 m. Average speed = 100.00 m / 10.5 s = 9.5238 m/s. 10.5 has three sig figs, 100.00 has five, so answer is 9.52 m/s (three sig figs).

Density of a gas: A gas at 25 °C fills a container whose volume is 1.05 × 10³ cm³. The container plus gas has a mass of 837.6 g. The container, when emptied, has a mass of 836.2 g. What is the density of the gas?

Mass of gas = (837.6 - 836.2) g = 1.4 g. In subtracting numbers, we determine sig figs by counting decimal places. Each mass has one decimal place, so 1.4 g has one decimal place.

Density = mass / volume = 1.4 g / 1.05 × 10³ cm³ = 1.3 × 10^-3 g/cm³ = 0.0013 g/cm³. In dividing, we count sig figs. There are two significant figures in the answer, corresponding to the smaller number of significant figures in the ratio. Notice that following the rules gives an answer containing only two significant figures, even though each of the measured quantities contained at least three significant figures. This shows how subtraction can drastically reduce precision.

If you want the density to be calculated to three significant figures, to how many significant figures should the mass of the container be measured? Five. For the difference in the two masses to have three significant figures, there must be two decimal places in the masses of the filled and empty containers. Therefore, each mass must be measured to five significant figures.

When a calculation involves two or more steps and you write answers for intermediate steps, retain at least one nonsignificant digit for the intermediate answers. This procedure ensures that small errors from rounding at each step do not combine to affect the final result. When using a calculator, you may enter the numbers one after another, rounding only the final answer. Accumulated rounding-off errors may account for small differences among results you obtain and answers given in textbooks for numerical problems.

Pro Tip for Exams:Carry one extra digit through all intermediate steps and only round at the very end. If you round at each step in a multi-step AP free response, you will lose the final accuracy point even if your method is perfect.

Exam Trap:The most common FRQ mistake: Using sig fig rules for addition when you should use multiplication rules. If you are adding masses then dividing by volume to get density, the subtraction step uses decimal places, but the division step uses sig figs. Students apply the same rule to the whole problem and lose marks.

Practice Questions

MCQs (Multiple Choice Questions)

01. Which of the following is an exact quantity?

1. The mass of a dime measured as 2.24 g
2. The number of students in a chemistry class counted as 24
3. The temperature measured as 27 °C
4. The volume measured as 1.05 × 10³ cm³

Correct: B
Explanation: Counted numbers are exact. Measured values (mass, temperature, volume) are always inexact and have limited significant figures. 24 students is exact with infinite sig figs.

02. A balance shows 0.0200 g. How many significant figures does this have?

1. 1
2. 2
3. 3
4. 4

Correct: C
Explanation: Leading zeros (0.0) are never significant. The zeros between 2 and the decimal and the trailing zeros after decimal point with decimal present are significant. So 2, 0, 0 are three sig figs.

03. Which measurement implies the greatest certainty?

1. 4.0 g
2. 4.00 g
3. 4 g
4. 4.0 ± 0.2 g

Correct: B
Explanation: More significant figures = greater certainty. 4.00 has three sig figs and implies uncertainty in hundredths (±0.01), while 4.0 implies ±0.1. 4 g implies ±1.

04. You measure 20.42, 1.322, and 83.1 and add them. What is the correctly rounded sum?

1. 104.842
2. 104.84
3. 104.8
4. 105

Correct: C
Explanation: For addition, result has same number of decimal places as measurement with fewest decimal places. 83.1 has one decimal place, so round to one decimal place: 104.8.

05. Area = 6.221 cm × 5.2 cm. Correct area is:

1. 32.3492 cm²
2. 32.35 cm²
3. 32 cm²
4. 32.3 cm²

Correct: C
Explanation: For multiplication, result has same number of significant figures as measurement with fewest sig figs. 5.2 has two sig figs, so result must have two: 32 cm².

06. How many significant figures are in 1005 kg?

1. 1
2. 2
3. 3
4. 4

Correct: D
Explanation: Zeros between nonzero digits are always significant. 1, 0, 0, 5 = four.

07. The number 5000. has how many significant figures?

1. 1
2. 2
3. 3
4. 4

Correct: D
Explanation: With a decimal point present, trailing zeros are significant. 5000. explicitly shows four. Without decimal, 5000 would be assumed to have one.

08. Which set of darts shows good precision but poor accuracy?

1. All darts in bullseye, tightly clustered
2. Darts tightly clustered in top left corner, away from bullseye
3. Darts scattered randomly across board
4. Darts scattered around bullseye

Correct: B
Explanation: Good precision = tightly clustered. Poor accuracy = far from true value (bullseye).

09. Density = 1.4 g / 1.05 × 10³ cm³. Correct density to proper sig figs is:

1. 0.001333 g/cm³
2. 0.0013 g/cm³
3. 0.00133 g/cm³
4. 1.3 × 10^-3 g/cm³ (two sig figs)

Correct: D (B and D are same value, D is better notation)
Explanation: Division uses fewest sig figs. 1.4 has two sig figs, 1.05 × 10³ has three, so answer must have two. 1.3 × 10^-3 g/cm³ has two.

10. When you perform a multi-step calculation, you should:

1. Round after each step to correct sig figs
2. Retain at least one extra nonsignificant digit in intermediate steps and round only at end
3. Use exact numbers only
4. Always report answer with three sig figs

Correct: B
Explanation: Rounding at each step causes accumulated rounding errors. Best practice is to carry extra digit and round only final answer.

FRQs (Free Response Questions)

FRQ 1: (AP/IB Style) A student measures the mass of a sample four times: 10.12 g, 10.13 g, 10.11 g, 10.12 g. The true mass is 10.00 g. Discuss precision and accuracy.

Rubric:

• States high precision because the values agree closely. Must mention small range of 0.02 g or small standard deviation (1 pt)
• States low accuracy / inaccurate because the average ∼10.12 g differs from the true value of 10.00 g by 0.12 g (1 pt)
• Mentions systematic error / calibration error as the likely cause (1 pt)
• Mentions how to improve: recalibrate the balance or check with a standard mass (1 pt)

FRQ 2: (A-Level Style) State number of significant figures in:
(a) 0.00260 m
(b) 6.02 × 10²³ mol^-1
(c) 400.
(d) Explain how to write 400 to show three significant figures.

Rubric:

• (a) 0.00260 m = 3 sig figs: Leading zeros are not significant, trailing zero with a decimal is significant (1 pt)
• (b) 6.02 × 10²³ mol^-1 = 3 sig figs: The exponential term does not count toward sig figs (1 pt)
• (c) 400 = 1 sig fig: By convention, trailing zeros without a decimal point are not significant (1 pt)
• (d) How to show three sig figs for 400: Must write as 400. or 4.00 × 10². Explanation must reference adding a decimal point or using scientific notation (1 pt)

FRQ 3: (College Chem) Calculate volume of cylinder with diameter 2.45 cm (measured with calipers) and height 15.1 cm. Radius = diameter/2. Show proper sig figs.

Rubric:

• Radius calculation: r = d/2 = 2.45/2 = 1.225 cm, correctly kept as 1.23 cm for 3 sig figs in intermediate step (1 pt)
• Correct formula: Uses V = πr²h (1 pt)
• Correct sig figs in final answer: V = π × (1.225)² × 15.1 = 71.19 → 71.2 cm³. Final answer limited to 3 sig figs because both diameter (2.45) and height (15.1) have 3 sig figs (1 pt)
• Correct unit: Includes cm³ (1 pt)

FRQ 4: (USNCO Style) In density experiment, mass of empty flask 36.2 g, mass with liquid 40.14 g, volume 20.0 mL. Calculate density with correct sig figs and explain limiting measurement.

Rubric:

• Subtraction rule: Mass of liquid = 40.14 - 36.2 = 3.9 g. Must apply decimal place rule, answer limited to one decimal place because 36.2 has one decimal place (2 pts)
• Division rule and final answer: Density = 3.9 g / 20.0 mL = 0.20 g/mL (accept 0.19-0.20). Must state that many students incorrectly give 0.195 g/mL and that the subtraction step is the limiting measurement. Final answer must have 2 sig figs (2 pts)

FRQ 5: (IB HL) A sprinter runs 100.00 m in 10.5 s. Calculate average speed. A second student says speed is 9.5238095 m/s because calculator shows that. Evaluate.

Rubric:

• Calculation: Speed = distance / time = 100.00 / 10.5 = 9.52 m/s (1 pt)
• Sig figs justification: Answer must be limited to 3 sig figs because time (10.5 s) has 3 sig figs, which is less than distance (100.00 m has 5) (1 pt)
• Evaluates calculator display: Explains that 9.5238095 m/s shows false precision, violates significant figure rules, and displays digits that are not significant (1 pt)
• Concept of uncertainty: States that a final answer must contain only one uncertain digit (1 pt)

Frequently Asked Questions

What is the difference between precision and accuracy in chemistry?

Precision is how close repeated measurements are to each other, showing reproducibility and small random error. Accuracy is how close measurements are to the true value, showing absence of systematic error. You can be precise but inaccurate if your instrument is poorly calibrated.

How do you determine significant figures?

Count from the first non-zero digit. All non-zero digits are significant. Zeros between non-zeros are significant, leading zeros are never significant, trailing zeros are significant only if a decimal point is present. Use scientific notation to remove ambiguity.

How many significant figures are in 0.0020?

Two significant figures. The leading zeros 0.00 are not significant, they only locate the decimal point. The 2 and the trailing 0 are significant because there is a decimal point. So 2.0 × 10^-3 has two sig figs.

What are the rules for significant figures in addition and subtraction?

The answer must have the same number of decimal places as the measurement with the fewest decimal places. For example, 20.42 + 83.1 = 103.5, because 83.1 has one decimal place. Count decimal places, not total sig figs.

What are the rules for significant figures in multiplication and division?

The answer must have the same number of significant figures as the measurement with the fewest significant figures. For example, 6.221 cm × 5.2 cm = 32 cm², because 5.2 has two sig figs. Count total sig figs, not decimal places.

Is a counted number exact?

Yes. Counting discrete objects gives an exact number with infinite significant figures. Twelve eggs in a dozen and 15 students counted in a class are exact. Defined conversion factors like 100 cm = 1 m are also exact.

Why is 4.0 g different from 4.00 g?

They imply different uncertainty. 4.0 g has two significant figures and means 4.0 ± 0.1 g. 4.00 g has three significant figures and means 4.00 ± 0.01 g. The second measurement is ten times more certain.

How do you round if the digit is exactly 5?

If the digit to be removed is less than 5, leave preceding digit unchanged. If 5 or greater, increase preceding digit by 1. Some textbooks use round-to-even for exactly 5 followed by zeros to avoid bias: 4.7350 becomes 4.74 and 4.7450 also becomes 4.74.

Do exact numbers affect significant figures in calculations?

No. Exact numbers have infinite significant figures and never limit the result. When you multiply by 12 inches in 1 foot, the 12 does not limit sig figs. Only measured, inexact numbers limit the final answer.

Exam Mapping

Concept	A-Level Chemistry (AQA/OCR/Edexcel)	AP Chemistry	IB Chemistry HL	College Chemistry 1 & 2	USNCO / IChO
Exact vs Inexact Numbers	Practical skills: identify measurement vs count	LO 1.1 - Distinguish types of data	Topic 1.1 - Uncertainty and error	Chapter 1 - Measurement classification	Lab practical - error analysis
Precision vs Accuracy	Required Practicals - evaluate method	Science Practice 5 - Argumentation	Paper 3 - Evaluate precision/accuracy of data	Error analysis in lab reports	High yield - identify systematic vs random
Significant Figures Rules	3.1.1 - Use appropriate number of sig figs in calculations	Must report answers with correct sig figs or lose points	Criterion for all quantitative answers	Fundamental - all chapters	Mandatory - points deducted for wrong sig figs
Addition/Subtraction Rule	Practical: recording burette readings to 0.05 cm3	FRQ scoring: decimal place rule	Significant figure rules in processing data	Chapter 1 calculations	Common trap in density, titration
Multiplication/Division Rule	All stoichiometric calculations	All stoichiometric, gas law, equilibrium calculations	All quantitative topics	All quantitative topics	All calculations
Rounding & Intermediate Digits	Mathematical skills	FRQ: avoid intermediate rounding	IA - avoid rounding errors	Lab - keep extra digit	Avoid accumulated error
Standard Deviation	A-Level Maths for Chemists - spread of data	Not heavily tested but concept of precision	Topic 11.1 - Standard deviation meaning	Optional advanced	Advanced camp

Conclusion

Uncertainty is not a flaw in chemistry, it is a feature of all experimental science. Every measurement you make is inexact and carries an implied uncertainty expressed through significant figures. By mastering the distinction between exact and inexact numbers, internalizing the difference between precision, which reflects random error and reproducibility, and accuracy, which reflects systematic error and calibration, and applying the two distinct rules for significant figures in calculations, you transform from a student who reports calculator digits to a chemist who reports meaningful data. Remember: addition and subtraction are governed by decimal places, multiplication and division by total significant figures, and exact numbers never limit you. Carry an extra digit through multi-step problems and round only at the end. Master this now and you will secure marks across every quantitative topic from stoichiometry to equilibrium.

References

• Brown, T. L., LeMay, H. E., Bursten, B. E., Murphy, C. J., Woodward, P. M., & Stoltzfus, M. W. Chemistry: The Central Science, 14th Edition. Pearson.
• IUPAC Guidelines on Reporting Uncertainty in Measurement.
• AP Chemistry Course and Exam Description - College Board - Unit 1: Atomic Structure and Properties.