Significant figure rules are really "rules of thumb" for how to handle the results of calculations so as not to introduce or lose precision in performing a mathematical operation. These rules are not always correct for all situations. However, in most cases, following the significant figure rules will yield a good result.

Rules concerning zero

A zero between two significant figures is significant. The number 203.2 consists of four significant figures. A Zero to the right of a digit beyond the decimal point is a significant figure. The number 14.720 consists of five significant figures. (Note the zero would not be necessary to set the decimal point, thus it is significant). A zero is not significant if it merely fixes the decimal point. The number 0.031 contains two significant figures, the zero sets the decimal point and is not significant. In the number 1200 the zeros may or may not be significant. The digits and zeros shown in the decimal part of standard exponential numbers are significant. 3.2 x 10-2 indicates two significant figures.

1.2 x 103 indicates two significant figures.
1.20 x 103 indicates three significant figures.
1.200 x 103 indicates four significant figures.

Addition or Subtraction

When adding or subtracting the last digit that is retained in the sum or difference corresponds to the least precise number used in the computation.

To add: 1) Add the numbers 2) round the sum to the lowest common digit.

Ex. 5.71 g
3.222 g
+ 1276. g
----------------
1276.932 g ~ 1277 g

Multiplication or Division

When multiplying or dividing the product or quotient should contain no more digits than the least number of significant figures in the number involved in the computation.

...SignificantFigures in Measurement and Calculations
A successful chemistry student habitually labels all numbers, because the unit is important. Also of great
importance is the number itself. Any number used in a calculation should contain only figures that are
considered reliable; otherwise, time and effort are wasted. Figures that are considered reliable are called
significantfigures . Chemical...

...on significantfigures
When we use an equipment to take measurement, it is important to be honest when reporting a measurement, so that it does not appear to be more accurate than the equipment used to make the measurement allows. To achieve this, we can control the number of significantfigures used to report the measurement.
When we look at a number, its first significantfigure is the first digit...

...be caught.
A. SIGNIFICANTFIGURES (10 pts.)
(Show the actual results first before rounding off the digits into their proper significantfigures.)
A.1. Determine the number of significantfigures in each numerical value below. (Assume all values are measurements.)
1. 357 ml
2. 1.0600 L
3. 0.000 501 g
4. 23, 000 tons
5. 1.8000 X 105 mi
A.2. Perform the following arithmetic...

...number of significantfigures indicated within brackets.
(a) 8.043 (2s.f.)
(b) 4.13865 (2s.f.)
(c) 0.04036 (1s.f)
(d) 0.03064 (3s.f)
(e) 64.074 (1s.f)
(f) 71.97 (3s.f)
(g) 2467 (2s.f)
10. Calculate the following and write correct to 1s.f
(a)
(b)
(c)(4.742+6.292)3
(d)
11. The diameter of the sun is 1 392 530
kilometres. Write this value correct to
4 significantfigures....

...example of physical change?
A. The rusting of an iron nail
B. The burning of propane in a gas grill
C. Baking cookies
D. Polishing tarnished silver
E. Melting of an ice cube in a glass of soda
3. Which measurement has the fewest number of significantfigures?
A. 12.80 m
B. 0.1280 m
C. 0.001280 m
D. 1280 m
4. Which quantity is an exact number?
A. 3 cars
B. 1,000 m
C. 2 L
D. 453.6 g
5. The number 0.0035880 expressed correctly using...

...glassware (beakers, burettes, pipettes, graduated cylinders, flasks, etc) should be used in various
circumstances.
2. Know how to “correctly” measure volume and mass (weight).
3. Become familiar with significantfigures and its relationship to measurements and data recording (significantfigures).
4. Become familiar with the errors, precision and accuracy associated the various measurement tools and techniques.
5. Determine the...

...allegedly authoritative number.
Significantfigures
Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m. To record this measurement as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many...

...unit
b) the ratio, by number, of C atoms to H atoms to 3 significantfigures
c) the ratio, by mass, of Ge to S to 3 significantfigures
d) the number of g S in 1 mol of the compound to 3 significantfigures
e) the number of C atoms in 33.10 g of the compound
5)
Determine the mass % O in the mineral malachite, Cu 2 (OH) 2CO3 .
6)
Determine the mass % H2O in the hydrate Cr(NO3 )3 ⋅ 9H 2O ....