Measurement

Measurements• science is based on

measurements• all measurements have:– magnitude– uncertainty– units

Numbers• mathematics is based

on numbers• exact numbers are

obtained by :– counting– definition

Measurements

• Measurements are not numbers– Numbers are obtained by counting or by

definition; measurements are obtained by comparing an object with a standard “unit”

– When you say that a table is 2 meters long, you are really saying that the table is two times longer than an object that is 1 meter long

Measurements

• Numbers are exact; measurements are inexact• Mathematics is based on numbers; science is

based on measurement

Uncertainty in Measurement

• Comparison with a unit or a scale of units always involves some uncertainty

• Estimate between the smallest scale divisions• The digit between the lines is always uncertain

(estimated)

Uncertainty in Measuring Devices

• There is a limit to the precision of a measurement

• The scientist making the measurement must decide the uncertainty value for a particular measuring device.

• See “Scale Reading, Uncertainty and Significant Figures”

Significant figures

• Significant figures are the digits in a measurement known with certainty plus one digit that is uncertain (estimated)