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 calculations involve numbers representing actual measurements. In a
measurement, significantfigures in a number consist of:
Figures (digits) definitely known + One estimated figure (digit)
In class you will hear this expressed as "all of the digits known for certain plus one that is a guess."
Recording Measurements
When one reads an instrument (ruler, thermometer, graduate, buret, barometer, balance), he expresses
the reading as one which is reasonably reliable. For example, in the accompanying illustration, note the
reading marked A. This reading is definitely beyond
the 7 cm mark and also beyond the 0.8 cm mark. We
read the 7.8 with certainty. We further estimate that
the reading is five-tenths the distance from the 7.8
mark to the 7.9 mark. So, we estimate the length as
0.05 cm more than 7.8 cm. All of these have meaning
and are therefore significant. We express the reading as 7.85 cm, accurate to three...

...Additional Notes 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 from the left, other than 0.
E.g. - in the number 539 the first significantfigure is 5
- in the number 0.06189 the first significantfigure is 6
The number of significantfigures is the number of digits counting from the left from the first significantfigures.
By looking at the examples below, generate some rules in determining the number of significantfigure of a number.
* in the number 0.06189 there are four significantfigures
* in the number 2390001 there are seven significantfigures
* in the number 2390000 there are three (or seven) significantfigures**
* in the number 2390000.00 there are nine significantfigures
The rules that I can generate are:
When...

...will 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 operations and express the answer to the correct number of significantfigures
1. 0.392 + 51.4
2. (5260 x 12.0) / 2.1
3. 273.15 – 28.3
4. 8.63 x 0.58
5. 6.02 / 3.0
B. SCIENTIFIC NOTATION (10 pts.)
B.1. Convert the following numbers from scientific notation to normal notation
1. 8.59 x 10 -3
2. 2.76 x 10 2
3. 2.76 x 10 -2
4. 7.2 x 109
5. 7.2 x 10-9
B.2. Convert the following numbers from normal notation to scientific notation
1. 0.000 000 000 8304
2. 9,500,000
3. 0.013
4. 58.3
5. 0.583
C. DENSITY and SPECIFIC GRAVITY (20 pts.)
(Observe proper SignificantFigures in the answer)
1. Calculate the mass in grams of 15.0ml of a saline solution that has a density 1.05 g/ml
2. Copper has a density of 8.96 g/ml. Calculate the volume occupied by 125.0 g of copper.
3. A. If the density of a liquid is 0.80 g/ml, what is its specific gravity?
B. If the...

...p)
5. An athlete’s time for a race was 43.78secods.
(a) Write this time correct to
(i) One decimal place
(ii) Correct to tens
(b) Write 43.78 and answers to (a) part (i) and (ii) in the ascending order.
6. Change to decimal. Write down calculator display correct to 4dp.
7. A car costs £7552. Write the cost of the car nearest 100pounds.
8. The mass of a bottle is 483gms. Write the mass correct to hundred grams.
9. Round off the following numbers correct to the 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.
12. Write the number 2381.597 correct to
(a) 3 significantfigures,
(b) 2 decimal places,
(c) the nearest hundred.
...

...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 scientific notation is
A. 0.0035889.
B. 3.5880 × 103.
C. 3.5880 × 10–3.
D. 3.5880 × 10–4.
6. The measurement 78,005,760 expressed correctly using scientific notation is
A. 7.8005760 × 107.
C. 7.8 × 107.
D. 7.800576 × 10–7.
E. 7.800576 × 107.
7. When 4.870 × 10–3 is correctly converted to its standard form the number becomes _____.
A. 4870
C. 0.00487
D. 0.004870
E. 0.0004870
8. Which number is the largest?
A. 4.38 × 103
B. 4.38 × 102
C. 4.38 × 10–3
D. 4.38 × 10–2
E. 438
9. Which number is the smallest?
A. 4.38 × 103
B. 4.38 × 102
C. 4.38 × 10–3
D. 4.38 × 10–2
E. 438
10. When 0.022189 is correctly rounded to two significantfigures the number becomes _____.
A. 0.02
B. 0.022
D. 0.023
11. When 5.5490× 108 is correctly rounded to three significantfigures the number becomes _____.
A. 5.55
B. 5.55 × 108
D. 554
E. 5.54 × 108
12. Which number has four significantfigures?
A. 3.978
B. 0.780
C. 0.0085
13. What is the correct answer to this calculation, reported using the proper number of significantfigures: 38.251 + 73.1?
A. 111
B. 111.3
C....

...Introduction to Chemistry Laboratory:
A Lesson on Tools, Techniques and Measurements
PURPOSE: The purpose of this set of experiments (3 total) is to become familiar with the common types of laboratory
glassware and equipment, and how to obtain and analyze data from these items.
LEARNING OBJECTIVES: By the end of this experiment, the student should be able to demonstrate the following
proficiencies:
1. Know which 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 density of liquids and solids.
6. Determine the best-fit straight line as a method to examine linear relationships and to use this relationship as a
predicative model such as in the determination of the percent copper and zinc in pennies based on density
measurements.
7. Record laboratory data and observations.
MATERIALS:
Erlenmeyer Flasks
o 125 mL
o 250 mL
beakers
o 100 mL
graduated cylinders
o 10 mL
o 25mL
Burette
o 50 mL
Volumetric pipettes
o 10 mL
Measuring pipet
o 10 mL
Burette clamp and stand
Various liquids and solids for density determination...

...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 manysignificantfigures as are consistent with the estimated error. The quantity 0.428 m is said to have three significantfigures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement in centimeters would be 42.8 cm and still be a three significantfigure number. The accepted convention is that only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m.
Students frequently are confused about when to count a zero as a significantfigure. The rule is: If the zero has a non-zero digit anywhere to its left, then the zero is significant, otherwise it is not. For example 5.00 has 3 significantfigures; the number 0.0005 has...

...sample consisting of 2.65 L liquid bromine (d = 3.10 g/mL)
3)
Explain which of the following statement(s) is (are) correct for sorbic acid, C6H8O2.
a) it has a C:H:O mass ratio of 3:4:1.
b) it has the same mass % composition as acrolein, C3H4O.
c) it has the same empirical formula as aspidinol, C12H16O4.
d) it has four times as many H atoms as O atoms, but four times as much O as H by mass.
4)
For the compound Ge[S(CH2)4CH3]4, determine
a) the total number of atoms in one formula 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 . Express your answer to 4
significantfigures.
7)
Determine the empirical formula of the rodenticide warfarin (a carbon-hydrogen-oxygen
compound), which consists of 74.01% C and 20.76% O by mass.
8)
Selenium forms two oxides. One has 28.8% O by mass and the other has 37.8% O. What are
the formulas of these two oxides?
9)
Adenine is a carbon-hydrogen-nitrogen compound with 44.45% C and 3.73% H by mass. It’s
molecular mass is 135.14 u. What is its...