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# Zumdahl Chapter 1: Uncertainty in measurement

Uncertainty in measurement
Measurement: obtained by using measuring device.
The measured volume is 20.15 ml (the # 5 is estimated)
Deferent values could be obtained by different person (See Table)

The 1st three numbers (20.1) remain the same → certain digits
The digit to the right of 1 must be estimated and therefore varies → uncertain digits
We report measurement by recording all certain digits plus 1st uncertain digit
Measurement always has some degree of uncertainty which depends on the precision of the measuring device.

Significant Figures of Measurement

1- All certain digits and the 1st uncertain digit.
2- The uncertainty in the last number is usually assumed to be ±1 unless otherwise indicated.

Examples:

1- 1.86 kg means 1.86 ± 0.01 kg

2- in figure shown :

Pipet → 25.00 mL- 25.00 ± 0.001 mL → 24.99 - 25.01 mL

Graduated cylinder → 25 mL - 25 ±1 mL → 24-26 mL

Precision and Accuracy
Accuracy: Term refers to the agreement of a particular value with the true value.
Precision: Term refers to the degree of agreement among several measurements.

Error Types
1- Random error (indeterminate error): means that a measurement has an equal probability of being high or low: occurs in the last digit.
2- Systematic error (determinate error): occurs in the same direction each time: always high or always low.
In figure shown below
A - Large random error
B - Small random but large systematic error
C - Small random error and no systematic error

Average of a series of precise measurement is accurate: average out the random error because of their equal probability of being high and low).