Significant Figures and Scientific Notation
I. Definition of significant figures:
It is the maximum precision (reliability of a measurement) for a measurement.
It contains all the digits that are known plus the next/first digit that is estimated.
II. Rules for reporting significant figures in any measurement:
1. All nonzero digits are significant.
Example: 123.45 mL has 5 significant figures (1,2,3,4,5).
2. Zero is significant when it is between nonzero digits.
Example: 123034 cg has 6 significant figures (1,2,3,0,3,4).
3. Zero is not significant when it is before the first nonzero digit.
Examples: 0.00123 mg has 3 significant figures (1,2,3).
4. Zero is significant when it is at the end of a number that has a decimal point.
Example: 789.0 km has 4 significant figures (7,8,9,0).
5. Zero is not significant when it is at the end of a number without a decimal point.
Example: 560 mm has 2 significant figures (5,6)
6. If a measurement is written in scientific notation, then all digits before the multiplication sign are significant figures.
Example: 1.23 x 108 L has 3 significant figures ( 1,2,3).
Example: 5.0 x 106 dag has 2 significant figures (5,0).
Sample problem using scientific exponential notation:
Original problem First & second calculator step (6.2x10-4) (5.04x107) (3.1x102 (2.9x107) Note: The calculator is set for scientific notation.
7. Conversion factors that allow one to change from English to metric (or metric to English) require one to determine the significant figure for each of the conversion factors . For any one conversion factor you will only use the numerator or denominator value that has more significant figures.
Example:
454 g = 1 lb (The 454 has 3 significant figures, ignore the 1 in the pounds value.)
2.54 cm = 1 in (The 2.54 has 3 significant figures.)
Sample problem: Convert 3.2 g/5.3 mL to lb/gal
2 2 3 2 3.2 g 1 lb 1.0x103 mL 3.79 L 1.2128 x104 1.0x104 lb 5.3mL 454 g 1 gal gal 2 3 Note: The number of significant figures are in brown.
8. One ignores the number of significant figures of the conversion factors when converting from metric to metric or from English to English.
Example:
Given Conversion factor 2 2 3.2 g 1 kg 3.2x10-3kg 1 1.0x103g Note: the significant figure(s) to be used are in brown.
Example:
Given Conversion factor 3 3 335 in 1 ft 2.79 x101ft 1 12 in Note: the significant figure(s) to be used are in brown.
9. Exact numbers are ignored when determining the number of significant figures.
III. Math with metric units.
1. When performing addition or subtraction operations, the number of significant figures in the answer is determined by the least number of places in each factor being added or subtracted.
thousandths place hundreths place tenths place calculator answer
2. When multiplying numbers with units such as centimeter (cm) both the number and the unit (metric / English) must be multiplied and the number of significant figures in the answer is determined by the factor with the least significant figure value.
Example:
= =
IV. Laboratory application.
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SELF QUIZ View the graduated cylinder (eye level with mark) to avoid error due to parallax. Your reading of the device should include all marked divisions and the first estimated place value. Since the graduate cylinder in the example is marked in 5 mL divisions, you can estimate to the 1 mL unit. What would the indicated volume for this example be in mL? (Use significant figures). Now express your answer in scientific notation. |
A reasonable answer would be 83 mL.
8.3 x 101