2. Dimensional Analysis
Any valid physical formula must be dimensionally consistent — each term must have the same “dimensions”
(You can think in terms of units rather than “dimensions” if you prefer)
Examples:
distance = velocity × time velocity = acceleration × time energy = mass × (velocity)2

3. Significant Figures Accuracy of measurements is limited
Significant figures: the number of digits in a quantity that are known with certainty

4. Significant Figures Accuracy of measurements is limited
Significant figures: the number of digits in a quantity that are known with certainty
Clicker Question: How many sig figs does this number have?
A) B) C) D) E) 7

5. Significant Figures Accuracy of measurements is limited
Significant figures: the number of digits in a quantity that are known with certainty
Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity
Example: What is…

6. Significant Figures Accuracy of measurements is limited
Significant figures: the number of digits in a quantity that are known with certainty
Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity
Example: What is…

7. Significant Figures Accuracy of measurements is limited
Significant figures: the number of digits in a quantity that are known with certainty
Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity
Example: What is…

8. Significant Figures Accuracy of measurements is limited
Significant figures: the number of digits in a quantity that are known with certainty
Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity
Example: What is…

9. Significant Figures Accuracy of measurements is limited
Significant figures: the number of digits in a quantity that are known with certainty
Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity
For addition or subtraction, line up the decimal points
Example: What is…

10. Scientific Notation
Leading or trailing zeroes can make it hard to determine number of significant figures: 2500,
Each of these has two significant figures
Scientific notation writes these as:
a number from 1– (the mantissa)
multiplied by a power of 10 (the exponent)
This makes the number of significant figures much clearer:
2500 = 2.5 × (two sig figs)
2500 = 2.50 × (three sig figs)
2500 = × (four sig figs)
On your calculator – use the scientific notation key, NOT the [10x] key !!!!

11. Round-off Error
Keep extra digits throughout your calculations – only round off at the end.
Two answers that are different only in the least significant digit (and usually only by 1) are probably the result of different rounding.