**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).