1

1.5 Uncertainty in Measurement

2

Measurements are always Measurements are always uncertain because measuring uncertain because measuring instruments are never flawless and instruments are never flawless and some estimation is always requiredsome estimation is always required

Example: A rulerExample: A ruler

3

The dark numbered lines represent The dark numbered lines represent centimeterscentimeters the thin lines are 0.1 cm or millimetersthe thin lines are 0.1 cm or millimeters

When reading the ruler you would read the When reading the ruler you would read the centimeters, then the tenth of the cm (mm) centimeters, then the tenth of the cm (mm) then estimate the last numberthen estimate the last number Example 2.45cmExample 2.45cm Written as 2.45  +/-0.01cmWritten as 2.45  +/-0.01cm

4

Measu

ring L

iquid

s &

M

enis

cus

Anim

ati

on

5

Reliability

Two ways to check you numbersTwo ways to check you numbers repeat the measurementrepeat the measurement test against a standardtest against a standard

Precision- how close the repeated Precision- how close the repeated measurements are to each othermeasurements are to each other

Accuracy-how close the Accuracy-how close the measurements are to a standard or measurements are to a standard or accepted valueaccepted value

6

Acc

ura

cy &

Pre

cisi

on

Dart

s A

nim

ati

on

7

Example

8

Sample Problem

Sara calculates the density of water to be Sara calculates the density of water to be 0.88g/ml, 0.87g/ml and 0.88g/ml on three 0.88g/ml, 0.87g/ml and 0.88g/ml on three trialstrials

Is she preciseIs she precise ? ? Yes, all close togetherYes, all close together

Is she accurate?Is she accurate? No, accepted value is 1 g/mlNo, accepted value is 1 g/ml