1. Chapter 3 - Measurements
UNIT 1 Foundations
Chapter 3 - Measurements

2. Chapter 3B Accuracy and Precision in Measuring

3. The Limits of Measuring
Measuring can never be exact, why?
Markings may not be in small enough increments to align exactly with the measurement
Environment conditions; temperature, pressure humidity may alter the scale
Observer may use or read the instrument wrong
Instrument may have defects
Instrument may be damaged
Conditions of measuring may interfere with getting a good measurement.

4. The Limits of Measuring
Every scientific measurement contains error!
The difference between a measurement and the dimension’s actual value
Try to minimize error by accuracy and precision

5. Accuracy
Accuracy
Evaluates how close a measurement is to the actual value
An assessment of the measurement error
Depends on how well the instrument is constructed and maintained
Must not change due to environmental conditions
Human error
Try to eliminate it by averaging multiple readings

6. Precision
Precision
Evaluates how exactly a measurement is made
An assessment of the exactness of a measurement
More precise means more digits, more digits mean better scale calibrations
Precision is limited to the size of the smallest subdivision on the instrument
If a quantity is defined or counted it is not measured and has infinite precision
Some measurements are read exactly, some are estimated
The estimated digit is the last digit

7. Significant Digits
Scientists have developed a system to communicate the precision of their measurements
Significant digits (or figures)
All the digits known from the instrument plus one estimated digit
Purpose is to establish the precision of the measurement, not its accuracy

8. Identifying Significant Digits
Rules – From now one all problems should have two answers: one normal, and one with significant figures
Only apply to measure data
Not counted or pure numbers
Not fractions that are considered to be 1 by definition
All nonzero digits
112.54m
34oC
3. All zeros between nonzero digits
10.6mL
15.06m
103K

9. Identifying Significant Digits
Decimals points define significant digits
All zeros to the right of the last nonzero digit are significant
45.0s
8.500L
If a decimal point is not present, no trailing zeros are significant
10cm
120oC
1800g
If a decimal point is present, none of the zeros to the left of the first nonzero digit are significant, leading zeros
0.050m

10. Identifying Significant Digits
Significant zeros in the one’s place are followed by a decimal point
110.m or 110m
1000.K or 1000K

11. Scientific Notation
Measurements in science often deal with very large or small numbers
Difficult to write, read and use
Numbers are more convenient if expressed in scientific notation
Format is M x 10n
M is a number greaten than or equal to 1 and less than 10
n is an integer (positive or negative)
All digits in M are significant
How can you make 3800 have three significant digits?
Can’t unless you use scientific notation!

12. Appendix E Calculations with Measurements

13. Adding and Subtracting Data
Rules – Deals with PRECISION
The data must have the same units
The precision of a sum or difference cannot be greater than that of the least precise data given
Example
Add 3.1m and 45 cm

14. Multiplying and Dividing Data
Rules – uses SIGNIFICANT DIGITS & PRECISION
A product or quotient cannot have more SDs than the measurement with the fewest SDs
The product or quotient of a measurement and a pure number has the same number of decimal places, or same precision as the original measurement
Examples
7 x 2.35cm = 16.45cm not 16.5cm
2.63 cm/5 = 0.53 cm not 0.526cm

15. Rounding Review Identify the place value you are going to round to
If the digit to the right is 0-4 then it is unchanged, 5-9 the number goes up
If the rounded place value is to the right of the decimal point, all digits to the right of the rounded number will be dropped; if it is to the left than the numbers turn into zeros.
Examples in brown box on page 72