Measurement

Exact Measurements

Where the values are known without any

estimation.

Examples of Exact Numbers• exactly 17 students in this class

• exactly 12 eggs in a dozen

• exactly 1000 g in a kilogram

• exactly 2.54 cm in an inch

• The number 1 in any conversion factor between units, as in 1 m = 100 cm is an exact number

Inexact Measurements

Values where some estimation is used to calculate. There is

some uncertainty.

Examples of Inexact

Numbers• Height• Weight• Length• Width

Any number obtained by measurement is always inexact.

Equipment Error

Inherent limitations in the equipment used to

measure quantities

Human Error

Differences in how different people make

the same measurement

Remember!!!

Uncertainties always exist in measured quantities!!!

What To Do, What To Do???

Search for Significance!

Use significant digits to indicate the accuracy of the measurement.

Significant FiguresWhen making

measurements, it is the size of the

measurement needed to be precise.

Sig. Fig. Rule

1)Non-zero numbers are always significant

2)Zeros between non-zero numbers are always significant.

3)All final zeros to the right of the decimal place are significant.

Sig. Fig. Rule4)Zeros that act as placeholders

are not significant.5)All numbers in calculations

should have same sig. fig. go with the smallest sig. fig. number

6)Counting numbers and defined constants do not change.

What’s the Sig. Fig.• 857

• 950

• 1800

• 45.2

• 45.0

• 92000.0

• 3

• 2

• 2

• 3

• 3

• 6

• 0.00243

• 505

• 0.0012300

• 3.22X105

• 1200.0060

• 0023

• 3

• 3

• 5

• 3

• 8

• 2

Scientific NotationExpresses numbers as a multiple of two factors-a

number between 1 and 10, and 10 raised to a power or exponent; makes it easier to write a really big number or

really small number.

Round to 3 sig. fig.• 15624• 17853• 19278• 17750• 17650• 24503• 276453

• 15600• 17900• 19300• 17800• 17600• 24500• 276000

Rounding Rules• If digit after sig # is above 5, then

round up• If digit after sig # is below 5 then

leave as is• If digit after sig # is 5 and # after

5 is not zero, then round up• If digit after sig # is 5 and # after

5 is zero; if sig # is odd round up and if even then leave as is.

Accuracy and Precision

Precision

Is the degree of exactness to which the measurement of a quantity can be reproduced

Accuracy

Is the extent to which a measured value agrees with the standard value of a quantity.

Precision and Accuracy

Percent Error

Scale

A determined measurement with a

distinct base line.

• 1018 exa E

• 1015 peta P

• 1012 tera T

• 109 giga G

• 106 mega M

• 103 kilo k

• 102 hecto h

• 101 deka da

• 10-1 deci d

• 10-2 centi c

• 10-3 milli m

• 10-6 micro µ• 10-9 nano n

• 10-12 pico p

• 10-15 femto f

• 10-18 atto a

Dimensional AnalysisA problem solving

method that focuses on the units that are

used to describe matter.

System International Units (SI Units)

Units are a name tag that lets you know what measurement

the number is for. The SI Units are the standard units use throughout the world.

SI Units• Time=

second (s)

• Length= meter (m)

• Mass= kilogram (kg)

• Temperature= Kelvin (K)

• Volume= liter (L) or cubic centimeter (cm3)

• Density= g/cm3