what is the measurement 222.008 mm rounded off to four significant digits?

Significant Figures and Units

Overview: In reporting numerical results, it is important to include the correct number of significant digits. While determining the right number of digits to include is a straightforward process, beginning students often overlook this of import particular. Hither we outline the rules involved in determining the appropriate number of digits to include when reporting results of calculations and experimental measurements.

Skills:

• Reporting scientific results with the appropriate number of significant digits.

New terms:

• Significant Figures
• Precision
• Accurateness

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Defining the Terms Used to Talk over Significant Figures

Meaning Figures: The number of digits used to express a measured or calculated quantity.
By using significant figures, nosotros can show how precise a number is. If we express a number beyond the place to which we accept actually measured (and are therefore certain of), we compromise the integrity of what this number is representing. Information technology is of import after learning and understanding significant figures to employ them properly throughout your scientific career.

Precision: A measure of how closely individual measurements concur with one another.
Accuracy: Refers to how closely individual measurements agree with the right or true value.

Digits that are Significant

1. Not-nothing digits are always pregnant.
2. Whatsoever zeros between 2 non-cypher digits are significant.
3. A final zero or trailing zeros in the decimal portion Just are significant.

Examples:

How many significant figures are in: 1. 12.548, 2. 0.00335, three. 504.seventy, 4. 4000

1. There are 5. All numbers are significant.
2. At that place are 3. The zeros are simply placeholders and locate the decimal. They are not trailing zeros. They are not significant.
3. At that place are v. The 2 zeros are not just placeholders. Ane is betwixt two significant digits and the other is a final, trailing cipher in the decimal portion. Hence, they are both significant.
4. This is a flake disruptive. It is somewhere between 1 and 4. In order to clarify, we need to convert this to scientific notation. If it were four 10 ten³, there is 1 meaning effigy. If it were iv.000 10 10³, and then at that place are four pregnant figures.

Rules for Using Pregnant Figures

• For addition and subtraction, the answer should have the aforementioned number of decimal places as the term with the fewest decimal places.
• For multiplication and division, the answer should have the aforementioned number of pregnant figures every bit the term with the fewest number of significant figures.
• In multi-pace calculations, yous may round at each step or but at the terminate.
• Exact numbers, such as integers, are treated as if they take an space number of significant figures.
• In calculations, round up if the first digit to be discarded is greater than 5 and circular down if it is below 5. If the offset discarded digit is v, then round up if a nonzero digit follows it, round down if information technology is followed by a zilch.

More Examples:

Addition and Subtraction. 12.793 + four.58 + 3.25794 = 20.63094

• With significant figures information technology is 20.63 since four.58 has 2 decimal places, which is the to the lowest degree number of decimal places.

Multiplication and Division. 56.937/0.46 = 130.29782609

• With meaning figures, the final value should be reported as 1.iii ten ten² since 0.46 has merely 2 pregnant figures. Observe that 130 would exist ambiguous, then scientific notation is necessary in this state of affairs.

Tidiness at the end of a calculation.

Then you take carried out a calculation that requires a series of seven or eight mathematical operations and at the end, later punching everything into your figurer, y'all see the outcome "fourteen.87569810512...". The question you should ask yourself is how many digits to include when reporting your final reply.

It is at this point that you must refer back to the quality of the data you were given (i.east., how many significant digits are included with the given data). We illustrate this here with one final example.

Iii scientists determine the mass of the same sample of FeCl₃. Scientist A works in a field laboratory and carries a portable residuum for determining the sample mass, the residuum can determine masses to the nearest +/- 0.i g. Scientist B has a ameliorate, but notwithstanding somewhat crude residual, which reports the mass to the nearest +/- 0.01 yard. Scientist C has a balance, like the analytical balances you will discover in chemical science laboratories at WU, that can determine sample masses to the nearest +/- 0.0001 g. If each scientist wants to indicate the total number of moles of FeCl₃ in the sample, how volition each do this in a way that reflects the precision of the instrumentation they are using? The 3 scientists all utilise the atomic masses suggested past IUPAC (International Union of Pure and Applied Chemistry), which are included in the tabular array below.

	Scientist A	Scientist B	Scientist C
given data	sample mass: nineteen.0 one thousand Atomic number 26 diminutive mass: 55.847 1000/mol Cl atomic mass: 35.4527 g/mol	sample mass: eighteen.99 m Fe atomic mass: 55.847 g/mol Cl atomic mass: 35.4527 g/mol	sample mass: 18.9925 one thousand Iron atomic mass: 55.847 g/mol Cl atomic mass: 35.4527 g/mol
reported moles FeClthree	0.117 mol FeCliii	0.1171 mol FeCliii	0.11709 mol FeCl3
Why?	The balance used for the mass determination limits the effect to iii significant digits.	The quality of the instrumentation is better, than that used by Scientist A, simply the result is still limited to merely 4 significant digits.	Why non 6 significant digits in the reported result? This time the reply is limited by the doubtfulness in the diminutive mass of Iron, which is known to 5 pregnant digits!

This brings upwards an interesting question. Why is the atomic mass of chlorine known to 6 meaning figures, while that of iron is but known to 5 pregnant figures? Click here for an caption.

More Examples

• Examples of rounding to the right number of meaning figures with a five as the showtime not-significant figure
  • Round 4.7475 to four significant figures: iv.747five becomes four.748 because the first non-meaning digit is 5, and we round the final significant effigy up to six to arrive even.
  • Round 4.7465 to 4 significant figures: four.7465 is iv.746 because the outset not-pregnant digit is v and since the last significant digit is even, we get out information technology lonely.
• An instance of a calculation where yous can "lose" significant figures doing an operation.

  The mass of ¹⁹F is 18.99840 u. How much mass is converted to energy when a ¹⁹F atom is assembled from its constituent protons, neutrons, and electrons?

  ¹⁹F 9 p⁺ + 9 e^- + 10 north⁰

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Source: http://chp090.chemistry.wustl.edu/~coursedev/Online%20tutorials/SigFigs.htm

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