1. Measurements in Experiments
The Science of Physics
Measurements in Experiments

2. Numbers as Measurements
To be of value, a measurement must have two parts in addition to the number
Dimension – what kind of quantity
Length, mass, time
Unit – how much of the quantity
Meter, kilogram, second

3. SI System Le Système International d’Unitès Used worldwide in science
Seven base units, each describing a single dimension
Units combine to form a derived unit
Liter, Newton, Joule, o Celcius

4. SI System Length – meter Amount of substance – mole Mass – kilogram
Electric current – Ampere
Time – second
Luminous intensity – candela
Temperature – Kelvin

5. SI Prefixes Used to accommodate extremes
Very large and small numbers
Can also use scientific notation

6. SI Prefixes Kilo As you move down the Hecta stairs, move the decimal
Deka right
base units
As you move deci
up the stairs, centi
move the decimal left milli

7. SI System Both dimension and unit must agree
Length is in meters, not in kilograms
When doing calculations with one dimension
Prefixes must be the same
Area=length*width
m*m not m*cm
25m*10m not 25m*1000cm

8. Accuracy and Precision
Accuracy – describes how close a measured value is to the true value of the quantity measured
Precision – refers to the degree of exactness with which a measurement is made and stated
How many decimal places there are
Do all of the measurements agree with one another

9. Significant Figures
Use significant figures to keep track of imprecision
Significant figures – those digits in a measurement that are known with certainty plus the first digit that is uncertain
When the last digit in a measurement is zero, it is difficult to tell if the zero is significant or not
You can use scientific notation to show that a zero is significant

10. Significant Figures Rules for Significant Figures
All non-zero digits are significant. (1-9)
Zeroes between significant digits are significant. (101, zero is significant)
Zeroes behind the decimal are significant if there is a non-zero number in front of them. (3.40, zero is significant)

11. Significant Figures Rules for Significant Figures
If there is a decimal point, zeroes at the end of a number are significant. (50. zero is significant)
Zeroes at the beginning of a number are not significant. (0.003, zeroes are not significant)
If there is no decimal point, zeroes at the end of a number are not significant. (60, zero is not significant)

12. Rules for Calculating With Significant Figures
Addition and Subtraction – answer should have same number of decimal places as the least amount of decimal places in the measurement
Multiplication and Division – answer should have the same number of significant figures as the measurement with the least amount of significant figures

13. Rules for Rounding Round down – 0-4 Round up – 6-9 Special Rules for 5
Round to the nearest even number if nothing follows the five (32.25 ≈ 32.2 or ≈ 54.8)
Round up if there are digits following the 5 ( ≈ 54.8)

14. Error Analysis Some error always exists in any measurement
Skill of the measurer and the precision of the instruments effect measurements
When reading an instrument, always estimate one more place than you are given
Multiple measurements minimizes the effects of experimental error

15. Error Analysis Mean – average
Mean = (sum of values) / (number of values)
Median – the value in the middle of the data when the data points are arranged in ascending order
Mode – the most common data point
Standard deviation – how far the data points vary with respect to the mean
Normal distribution – a typically bell shaped curve when the data is graphed where most data falls within one or two standard deviations of the mean
Outliers – any data points not within two standard deviations of the mean

16. Error Analysis
Percent Error – used to compare an individual or average experimental value to the correct or accepted value
Calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value and multiplying by 100%

17. Error Analysis
Percent error is positive if the accepted value is greater than the experimental value
Percent error is negative if the accepted value is less than the experimental value
Percent Error = (Experimental Value – Accepted Value) / Accepted Value * 100%