Help me with SIG-FIGS!!!?

Question

I really have no idea about the sig figs. Can you explain me about the calculations- addition, subtraction, multiplication and division of the sig-figs.

Answer 1

Here's how my chemistry teacher taught me:

All non-zero digits are significant.
ex: 123 = 3 sig figs; 2.3964 = 5 sig figs; 2,378 = 4 sig figs

All zeros between non-zero digits are significant.
ex: 102 = 3 sig figs; 20.6 = 3 sig figs; .3098 = 4 sig figs; 22.04 = 4 sig figs; 100,785 = 6 sig figs; 3.0042 = 5 sig figs

All zeros to the right of a non-zero digit are significant if a decimal point is present somewhere in the number.
ex: 3.0 = 2 sig figs; 34.20 = 4 sig figs; .2000 = 4 sig figs; 30.00 = 4 sig figs; 20. = 2 sig figs; 300. = 3 sig figs

All zeros to the left of the first non-zero digit are insignificant.
ex: 0.378 = 3 sig figs; 0.02467 = 4 sig figs; 0.000002 = 1 sig fig

All zeros in the ones place that don't precede a decimal point are insignificant.
ex: 40 = 1 sig fig; 350 = 2 sig figs

Zeros higher than the one's place that are not to the left of a non-zero digit or a decimal point may or may not be significant.
ex: 4,100 = either 2 or 3 sig figs; 310,000 = either 2, 3, 4, or 5 sig figs; 805,000 = either 3, 4, or 5 sig figs

Scientific notation allows us to eliminate placeholders and only express significant figures.
ex: 4.10 x 10^3 = 3 sig figs; 7.096 x 10^8 = 4 sig figs

When adding values, add them all up, and then round your answer to the least number of decimal places in the problem.
ex: 43.9 m + 23.84 m = 67.7 m, because in the problem, 43.9 only had one decimal place (it was the least in the problem), so your answer should also only have one decimal place.

When multiplying values of different sig figs, multiply them, and round them to the least number of sig figs in the problem.
ex: 23 m + 387.4 m = 410 m, because in the problem, 23 only had 2 sig figs (the least in the problem), so your answer should only have 2 sig figs.

Answer 2

Sig Figs With Decimals

Answer 3

Significant figures are really important for keeping a general sense of accuracy in the real word. The rule is basically, you cannot make a computation that is more accurate than your least accurate measurement.

For instance, if you made a mesurement of 1.56 grams and a measurement of 35.329 cubic centimeters and you wanted to figure out the density... You could do the math and get 0.0441563587987205 g/cc but that answer would be more accurate than the measurement you made. You look a measurement with the fewest sig figs (1.56 g) and you reduce you answer to just three significant figures.

.0442 g/cc

How do you know how many sig figs you have? Here's a quote from Wikipedia that may help:

Determining significant figures
Significant figures conventionally follow certain sets of rules. Such that:

All non-zero digits are significant: for example, 87.636 has five significant figures. In addition, any zeros that are between non-zeros are also considered significant; for example, 40.02 has four significant figures. Any zeros that follow immediately to the right of the decimal place in numbers whose absolute value is smaller than one are not considered significant, e.g., 0.00057 has two sf. The situation regarding trailing zero digits that fall to the left of the decimal place in a number with no digits provided that fall to the right of the decimal place is less clear, but these are typically not considered significant unless the decimal point is placed at the end of the number to indicate otherwise (e.g., "2000." versus "2000"). However, any zeros that follow the last non-zero digit to the right of the decimal point are significant, e.g.: 0.002400 has four significant figures.

Conventionally, a number with value 0 is considered to have one significant figure.

Answer 4

This Site Might Help You.

RE:
Help me with SIG-FIGS!!!?
I really have no idea about the sig figs. Can you explain me about the calculations- addition, subtraction, multiplication and division of the sig-figs.

Answer 5

No physical measurement is ever exact. The accuracy is always limited by the degree
of refinement of the apparatus used to make the measurements and by the skill of the
observer. Correct representation of data and results is important.

A significant figure is defined as one that is known to be reasonably trustworthy .
One estimated or doubtful figure is retained and regarded as significant in reading a
physical measurement.

In the reading of a length measurement made with an ordinary meter stick, a certain
length may be recorded as: 5.43 cm. In this reading the final digit is an estimate of a part
of a millimeter division on the scale. Perhaps the estimated 3 at the end should be as high
as 5 or as low as 1; in any case it indicates something about the length and is useful. This
reading has three significant figures. The location of the decimal point has nothing to do
with the number of significant figures. The reading just cited could be written as 54.3 mm
or as 0.0543 m. Although the decimal point has been shifted, the number of significant
figures is three in each case and the last figure has some uncertainty attached to it.

The presence of a zero in a datum is sometimes troublesome. If it is useful merely to
indicate the location of the decimal point, it is not called a significant figure, as in 0.0543
m/ if it is between two significant digits, as in a temperature reading of 30.40, it is always
significant. A zero digit at the end of a number tends to be ambiguous. In the absence of
specific information one cannot tell whether it is there merely to locate the decimal point or
because it is the best estimate. In such cases the true situation can be best expressed by
writing the correct number of significant figures multiplied by the proper power of 10. A
measurement of the speed of light, 186,000 mi/sec may be written 1.86 x 10^5 mi/sec, since
the value includes only three significant figures. If we agree to use scientific notation to
avoid ambiguity, then our rule simplifies to
ZEROES ON THE LEFT ARE NOT SIGNIFICANT, ALL OTHERS ARE.
It is just as important to include a zero at the end of a number as to include any other
digit that is significant. If in a reading of a meter stick one can estimate a fraction of a
millimeter, a reading of 20.00 cm is quite proper; it means that the last zero is the
considered reading of the observer. In such a case it would be incorrect to record the
reading as 20 cm since this would imply that the reading was taken only to the nearest
centimeter. The recorded figure should always express the degree of accuracy of the
reading.

Rules for Computation

In the computations involving measured quantities the process is greatly simplified
without any loss of accuracy if figures that are not significant are dropped.

Rule I In addition and subtraction, carry the result only through the first column (that is,
the first decimal place) that contains a doubtful figure. We do not count significant
figures when we do addition or subtraction.

Rule II In multiplication and division, carry the result to the same number of significant
figures that are in the factor with the least number of significant figures.


Example: Consider a rectangle whose sides are measured as 10.773 cm and 3.55 cm.
When these lengths are added 10.773
3.55
14.323
We keep only the hundredths place and express the answer as 14.32 cm.
If we were to multiply these two values to get the area, the calculator gives 38.24415.
Since we only have 3 sig. fig. in one of the numbers, our answer is only valid to 3 sig. fig.
Report the area as 38.2 cm2 .

When insignificant figures are dropped, retain the last figure unchanged if the first
figure dropped is smaller than 5. Increase it by 1 if the first figure dropped is greater than
5. If the dropped figure is exactly 5, leave the preceding digit unchanged if it is even, but
increase it by 1 if it is odd. Thus 3.455 becomes 3.46; 3.485 becomes 3.48; 6.7901
becomes 6.790.
Certain numbers that commonly appear in calculations have a peculiar relationship in
that they appear by definition rather than by measurement. Such numbers are assumed to
have an unlimited number of significant figures. The numbers 2 and pi in the expression 2 pi r
for the circumference of a circle are examples of such numbers.


Practice Problems:

1. Assuming that the following numbers are written with the correct number of
significant figures, make the indicated computations, carrying the answers to the correct
number of significant figures:

a. add 372.6587, 25.61, and 0.43798

b. 24.01 x 11.3 x 3.1416

c. 3887.6 x 3.1416/25.4

d. (12) x (10) / (40)

2. The following computations are arithmetically correct but the results are not properly
recorded because no attempt has been made to eliminate figures that have no significance.
Assume that the last digit in each of the numbers on the left of the equality sign is doubtful
and rewrite the answers so that all the figures retained have significance.

a. (1.732) (1.74) = 3.01368

b. (10.22) (0.0832) (0.41) = 0.34862464

c. (6.23)^2 = 38.8129

d. 628.7/7.6 = 82.72368421

e. 1624 + 478.27 + 1844.4 + 87.2 = 4033.87

f. (38.4 + 14.25) (0.87) = 45.80550

g. (17.34 - 17.13) (14.26) = 2.9946 (careful here)

h. (81.4) (1.628)/0.00000440 = 30,118,000

i. (12.5) (3.50) (.045714) = 1.9999875



--------------------------------------------------------------------------------

S2 Significant Figures Requirements

There are three types of question on the sig. fig. quiz.

One requires you to look at a given number and determine how many significant
figures are in that number. (Example .001703 has 4 significant figures)

Another requires you express a given value to some specified number of
significant figures including the proper round off.
(Example: Express 1.555507 to 4 sig figs.: Answer 1.556)
Numbers may be expressed in scientific notation in either the question or your
answer.

The last type requires you to perform a mathematical operation and express the
answer with the number of significant figures appropriate to calculation.

Examples

1) Add 3.1245
+12.33
Result: 15.45 (keeping only 2 decimal places here)


2) Evaluate (2.44)(1.8652)/(2.8) = ? (Ans.: 1.6 keeping only 2 sig. fig here)

Answer 6

well sig figs are like tig nigs, wheb you have 1 tignig you must surely have 1 sig fig you dig?

Answer 7

http://www.ric.edu/bgilbert/s2sigfig.htm