M EASURES : S IGNIFICANT FIGURES, PRECISION AND ACCURACY Dr. Chin Chu Chemistry River Dell High School.

MEASURES:SIGNIFICANT FIGURES, PRECISION AND ACCURACY

Dr. Chin Chu

Chemistry

River Dell High School

MEASUREMENTS

Temperature demonstration

What have been learned here? Human senses are not reliable indicator of

physical properties. We need instruments to give us unbiased

determination of physical properties. A system must be established to properly

quantify the measurements. Scales and units.

MEASUREMENTS

Definition – comparison between measured quantity and accepted, defined standards (SI).

Quantity: Property that can be measured and described by

a pure number and a unit that refers to the standard.

MEASUREMENT REQUIREMENTS

Know what to measure.

Have a definite agreed upon standard.

Know how to compare the standard to the measured quantity. Tools such as ruler, graduated cylinder, thermometer, balances and etc…

MEASUREMENTS – UNITS SI Units – (the metric system)

Universally accepted Scaling with 10

Base Units: Time (second, s) Length (meter, m) Mass (kilogram, kg) Temperature (Kelvin, K) Amount of a substance (mole, mol) Electric current (ampere, A) Luminous intensity (candela, cd)

MEASUREMENTS - TEMPERATURE Temperature Scales:

Celsius (°C, centigrade) Water freezing: 0 °C Water boiling: 100 °C

Kelvin (K, SI base unit of temperature) Same spacing as in Celsius scale. Conversion: Celsius + 273 = Kelvin

Fahrenheit (°F) Not the same spacing as the other two. Conversion: Fahrenheit = (5/9)(Celsius -32)

MEASUREMENTS – UNITS

Derived Units: Volume

Units: (length)3, such as cm3,m3, dm3 (liter)

Density Defined as mass per unit volume the substance occupies.

volume

massdensity

depthheightlengthvolume

HOW RELIABLE ARE MEASUREMENTS?

Let’s use a golf anaolgy

Accurate? No

Precise? Yes

Accurate? Yes

Precise? Yes

Precise? No

Accurate?Maybe?

Accurate? Yes

Precise? We cant say!

IN TERMS OF MEASUREMENT

Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across.

Were they precise? Were they accurate?

ASSESSING UNCERTAINTY

The person doing the measuring should asses the limits of the possible error in measurement

SIGNIFICANT FIGURES (SIG FIGS)

How many numbers mean anything When we measure something, we can (and do)

always estimate between the smallest marks.

21 3 4 5

SIGNIFICANT FIGURES (SIG FIGS)

The better marks the better we can estimate. Scientist always understand that the last number

measured is actually an estimate

21 3 4 5

object

mm

SIGNIFICANT DIGITS AND MEASUREMENT

Measurement Done with tools The value depends on the smallest subdivision

on the measuring tool

Significant Digits (Figures): consist of all the definitely known digits plus one

final digit that is estimated in between the divisions.

SIGNIFICANT FIGURES

Only measurements have significant figures. Counted numbers and defined constants are exact

and have infinite number of significant figures. A dozen is exactly 12 1000 mL = 1 L

Being able to locate, and count significant figures is an important skill.

Measured Value

Uncer- tainty

Ruler Division

Known digits

Estimated digit

1.07 cm +/-0.01 cm

0.1 cm 1, 0 7

3.576 cm +/-0.001 cm

0.01 cm 3,5,7 6

22.7 cm +/- 0.1 cm 1 cm 2, 2 7

Significant Figures: Examples

SIGNIFICANT FIGURES: EXAMPLES

What is the smallest mark on the ruler that measures 142.15 cm? ____________________

142 cm? ____________________

140 cm? ____________________

Does the zero count? We need rules!!!

RULES OF SIGNIFICANT FIGURES

Pacific:

If there is a decimal point present start counting from the left to right until encountering the first nonzero digit. All digits thereafter are significant.

Atlantic:

If the decimal point is absent start counting from the right to left until encountering the first nonzero digit. All digits are significant.

RULES OF SIGNIFICANT FIGURES - EXAMPLES

Pacific Ocean Atlantic OceanExample 1

Example 2

0.00078638

decimal point

7863800078638

No decimal point

78638

ROUNDING RULES

Rounding is always from right to left. Look at the number next to the one you’re

rounding. 0 - 4 : leave it

5 - 9 : round up

With one exception: when the number next to the one you’re rounding is 5 and not followed by nonzero digits (a.k.a. followed by all zeros) – round up if the number (rounding to) is odd; don’t do anything if it is even.

2.536

ROUNDING RULES - EXAMPLES

Example 1 2.532

Last significant digit

< 5 2.532.532leave it

Example 2 2.536

Last significant digit

> 5round up

2.54

2.5351Example 3 2.5351

Last significant digit

> 5round up

2.54

2.5350Example 4 2.5350

Last significant digit

the exception round up

2.54odd

MATHEMATICAL OPERATIONS INVOLVING SIGNIFICANT FIGURES

Addition and Subtraction

The answer must have the same number of digits to the right of the decimal point as the

value with the fewest digits to the right of the decimal point.

Why?

The result from the addition or subtraction would have the same precision as the least

precise measurement.

MATHEMATICAL OPERATIONS INVOLVING SIGNIFICANT FIGURES

Addition and Subtraction

Example:

28.0 cm23.538 cm25.68 cm77.218 cm

28.0 cm 23.538 cm 25.68 cm

1. Arrange the values so that decimal points line up.

4. Round the answer to the same number of places.

2. Do the sum or subtraction.

3. Identify the value with fewest places after decimal point.

77.2 cm

MATHEMATICAL OPERATIONS INVOLVING SIGNIFICANT FIGURES

Multiplication and Division

The answer must have the same number of significant figures as the measurement with

the fewest significant figures.

MATHEMATICAL OPERATIONS INVOLVING SIGNIFICANT FIGURES

Multiplication and Division

Example:

16924.76352 cm3

1. Carry out the operation.

2. Identify the value with fewest significant figures.

3. Round the answer to the same significant figures.

28.0 cm 23.538 cm 25.68 cm

28.0 cm23.538 cm25.68 cm

16900 cm3

3