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Significant figures are the digits in a number that contribute to its precision. They are important in scientific measurements and calculations because they convey the accuracy of the values being used. When reporting results, using the correct number of significant figures ensures that the precision of the data is communicated accurately. 

1. Non-zero digits: All non-zero digits are always significant.

   • Example: In the number 123.45, all five digits are significant.

2. Leading zeros: Zeros that precede all non-zero digits are not significant. They merely indicate the position of the decimal point.

   • Example: In 0.00456, only the digits 4, 5, and 6 are significant (3 significant figures).

3. Captive zeros (zeros between non-zero digits): These zeros are always significant.

   • Example: In 1002, all four digits are significant (4 significant figures).

4. Trailing zeros in a decimal number: These zeros are significant because they indicate the precision of the measurement.

   • Example: In 45.600, all five digits are significant (5 significant figures).

5. Trailing zeros in a whole number without a decimal point: These are usually not considered significant unless specified by a bar, underline, or scientific notation that indicates precision.

   • Example: In 2000, only one digit (2) is significant unless otherwise noted.

Rules for Calculations with Significant Figures

• Addition and Subtraction: The result should have the same number of decimal places as the number with the least decimal places.

• Multiplication and Division: The result should have the same number of significant figures as the number with the fewest significant figures.

Think you Understand?

5 has ___ significant figure(s).

82 has ___ significant figure(s).

900 has ___ significant figure(s).

408 has ___ significant figure(s).

125.39 has ___ significant figure(s).

0.00451 has ___ significant figure(s).

52.00 has ___ significant figure(s) and ___ decimal(s).

0.00073 has ___ significant figure(s) and ___ decimal(s).

7.340 has ___ significant figure(s) and ___ decimal(s).

0.07080 has ___ significant figure(s) and ___ decimal(s).

Dimensional analysis is a method used in science and engineering to analyze relationships between different physical quantities by identifying their fundamental dimensions (such as length, mass, time) and units of measure (such as meters, kilograms, seconds). It involves using these dimensions to check the consistency of equations, derive formulas, and convert units. 

Dimensional analysis is used to convert between different units of the same physical quantity. 

Unit Conversion: Dimensional analysis is used to convert between different units of the same physical quantity.

• Example: To convert 50 kilometers per hour (km/h) to meters per second (m/s), you use the following steps: