1. Measurement & Significant Figures
Metric System
Uncertainty in Measurement
Scientific Notation
Precision vs Accuracy
Significant Figures
Mathematics of Significant Figures
Trigonometry
In-class Homework:

2. Measurement and the Metric system
The metric system is consistently used worldwide within the Scientific Community
It is simple, easy to convert units and based on some of the properties of Water
1000 cm3 = ml =1000 g

3. Metric Prefixes Mega = 1,000,000 Kilo = 1000 Hecto = 100 Deka = 10
Deci = 1/10 (0.1)
Centi = 1/100 (0.01)
Milli = 1/1000 (0.001)
Micro = 1/1,000,000 ( )
Nano = 1/1,000,000,000 (1.0 x 10-9)

4. Uncertainty in Measurement
Every time we make a measurement we bring with it a certain amount of error (i.e. mechanical error, human error, parallax error.The whole purpose of significant figures and the mathematical operations we use with significant figures is based upon accounting for this uncertainty every time we make a measurement.

5. Scientific Notation
Scientific Notation is a system we use to display very large or very small numbers.
All scientists follow the same STYLE of reporting in scientific notation.
1.23 x 10n where the number is always between and time to raised to some exponent (n) which is positive for large values and negative for small values.

6. Scientific Notation (cont)
One of the nice things about scientific notation, is the number value tells you EXACTLY how many significant figures you have.
Remember if multiplying values in scientific notation, multiply the numbers, add the exponents and write the answer using proper notation. For Division, you subtract the exponents. EASY !

7. Precision vs. Accuracy
When making measurements, it is important to distinguish between making precise measurements and having accurate measurements.
PRECISION is defined simply as the number of decimal places a measured value goes out. (i.e cm is a more precise value than 12.4 cm). It has more scaled divisions on the device.
In order for a measurement to be ACCURATE, it must be compared to some STANDARD value.

8. Accuracy of Measurements
Measured Values
gm/ml
1.123 gm/ml
0.99 gm/ml
Standard Value
1.000 gm/ml
In this example, the value 0.99 gm/ml is the most ACCURATE
measured value because it is CLOSEST to the Standard value of
1.000 gm/ml.
Accuracy of measurements is always done by COMPARING the
measurements to some standard.

9. Whenever we are making any kind of measurement on a device:
Significant Figures
Whenever we are making any kind of measurement on a device:
We will read every scaled division on the device, and ESTIMATE THE LAST DIGIT

10. Definition of a significant figure
Any digit read or estimated from a scale on a measurement device.

11. Examples
Any non-zero number will always be significant. (43.21 has 4 significant figures)
Any zero between two non-zero numbers will always be significant (308 has 3 significant figures)
Zeroes only used as place holders are NOT significant ( has 3 sig figs)
Zeroes after non-zero numbers after the decimal point are always significant ( has 6 sig figs)

12. Math of Sig Figs
Since we read every scaled division and estimate the last digit, there is uncertainty in that last digit.
If we read a length as cm, that really means the length is somewhere between and cm, since the last digit was estimated.
When we perform mathematical operations on measured values, we need to treat significant figures carefully, so we do not make the answers more precise than the devices can measure.

13. Math of Sig Figs (cont)
There are two (2) rules for mathematical operations with significant figures:
1. Multiplication and Division: When multiplying and/or dividing, simply do all the mathematical operations and get your answer, then look back at the original values and count sig figs. Your answer can only have the least number of sig figs as your original values.

14. Math of Sig Figs (cont.)
2. Addition and Subtraction: If you are adding or subtracting measured values you will handle them MUCH differently than multiplication/division. First, line up the decimal points of all your measured values. Next, moving from left to right, go out to the value that is the LEAST precise (fewest number of decimals past the decimal point).

15. Addition/Subtraction of Sig Figs
Draw a vertical line there. We will call that the wall of significance and our answer will only go out to that number of places past the decimal point.
It is confusing at the beginning, but practice will definitely help you.
Refer to the Significant Figures Handout for examples.

16. Trigonometry q A Sin q = opp/hyp = a/c Cos q = adj/hyp = b/c
Tan q = opp/adj =a/b c a
q A b
a2 + b2 = c2

17. In Class Homework
Now let’s get some practice on the use of significant figures, scientific notation, trigonometry, precision and accuracy.