MEASUREMENT

Cartoon courtesy of Lab-initio.com

2 types of measurement

Qualitative-a non-numerical description of matter.(ex: red stone, heavy brick, hot steel)

Quantitative- a numerical measure. It must include a number, followed by a unit.

(ex: 2.14 grams, 49.6 ml, 0.2500 kg)

Uncertainty in Measurement

A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Why Is there Uncertainty? Measurements are performed with instruments

No instrument can read to an infinite number of decimal places

Which of these balances has the greatest uncertainty in measurement?

Taking Measurements

When taking measurements:Read to the smallest increment(mark) on the

instrumentEstimate one digit past the smallest

increment(mark)

Reading the Graduated Cylinder

Liquids in glass and some plastic containers curve at the edges

Changing the diameter of the cylinder will change the shape of the curve

This curve is called the MENISCUS

Your eye should be level with the top of the liquid

Reading the Graduated Cylinder

You should read to the bottom of the MENISCUS

Use the smallest increments to find all certain digits, then estimate 1 more digit.

There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are…

mL.

Estimate the uncertain digit and take a reading

The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is .

The volume in the graduated cylinder is

0.8 mL

mL.

10 mL Graduated CylinderWhat is the volume of liquid in the graduate?

___mL

25mL graduated cylinder What is the volume of liquid in the graduate?

___mL

100mL graduated cylinder What is the volume of liquid in the graduate?

____mL

What is this reading?

Practice Reading the Graduated Cylinder

___ ml

What is this reading?

Practice Reading the Graduated Cylinder

____ ml

Measuring Liquid Volume

Imag

es

create

d a

t htt

p:/

/ww

w.s

tand

ard

s.d

fes.

gov.

uk/p

rim

ary

fram

ew

ork

/dow

nlo

ad

s/S

WF/m

easu

ring

_cylin

der.sw

f

What is the volume of water in each cylinder?

Pay attention to the scales for each cylinder.

Reading a graduated cylinderAll of the equipment below measures volume in mL but the scales for each are different.

___mL ____mL ___mL

Reading a BuretOn the graduated cylinder, zero

was at the bottom of the scale, with values increasing going up the cylinder. However, a buret has zero at the top with values increasing going down the scale.

Determine the scale. Read at the bottom of the

meniscus with your eye level with the liquid.

____mL

What is the volume in the buret?

What is the volume in the buret?

Online Practice

Reading a graduated cylinder http://w1imr.cnm.edu/apps/chemlab/reading_a_meniscus.swf

Reading a buret http://w1imr.cnm.edu/apps/chemlab/burette.swf

Reading a ruler http://w1imr.cnm.edu/apps/chemlab/reading_a_ruler.swf

Lets play darts!

Precision and AccuracyAccuracy how close a result is to its true value.

Precision refers to the repeatability of results.

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate

Types of Error

Error- the difference between a measurement and the accepted value.

Random Error - measurement has an equal probability of being high or low.

Systematic Error – a repeated error, often resulting from poor technique or incorrect calibration.

Scientific Notation

In science, we deal with some very LARGE numbers:

1 mole = 602000000000000000000000

In science, we deal with some very SMALL numbers:

Mass of an electron =0.000000000000000000000000000000091 kg

Scientific Notation

Imagine the difficulty of calculating the mass of 1 mole of electrons!

0.000000000000000000000000000000091 kg x 602000000000000000000000

???????????????????????????????????

Scientific Notation:A method of representing very large

or very small numbers in the form:

M x 10n

M is a number between 1 and 10

n is the exponent

2 500 000 000

Step #1: Insert an understood decimal point

.

Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bounce the decimal point

123456789

Step #4: Re-write in the form M x 10n

2.5 x 109

The exponent is the number of places we moved the decimal.

0.0000579

Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bounce the decimal pointStep #4: Re-write in the form M x 10n

1 2 3 4 5

5.79 x 10-5

The exponent is negative because the number we started with was less than 1.

Convert each standard number to scientific

notation:

2000 g 0.972 m

880000 m 6.55 s

0.00821 kg 71.9 ms

96.3 g 8999 cm

0.000965 m 450 g

Convert each to floating decimal form:

7.00 x 102 m 17 x 100 cm

2.22 x 10-4 cm 3.00 x 108 m/s

9.45 x 10-8 m 6.02 x 1023 atoms

4.00 x 103 g 8.75 x 10-1 m

5.99 x 10-5 kg 6.78 x 10-6 m

Significant Figures-all the digits that are known to be true.

Rules for Counting Significant Figures - DetailsNonzero Digits(1-9) always count as significant figures.

3456 has 4 significant figures

Rules for Counting Significant Figures - Details

Zeros- Leading zeros never count as

significant figures.

0.0486 has3 significant figures

Rules for Counting Significant Figures - Details

Zeros- Captive

zeros(sandwiched zeros) always count as significant figures.

16.07 has4 significant figures

Rules for Counting Significant Figures - Details

ZerosTrailing zeros are significant only if the number contains a decimal point.

9.300 has4 significant figures

Rules for Counting Significant Figures - DetailsExact numbers have an infinite number of significant figures. They tend to be numbers of indivisible objects.

7 computers

or

1 inch = 2.54 cm, exactly

Sig Fig Practice #1How many significant figures in each of the following & which is the estimated digit?

1.0070 m 5 sig figs(0)

17.10 kg 4 sig figs(0)

100,890 L 5 sig figs(9)

3.29 x 103 s 3 sig figs(9)

0.0054 cm 2 sig figs(4)

3,200,000 2 sig figs(2)

Rules for Significant Figures in Mathematical Operations

Multiplication and Division: # sig figs in the answer equals the least number of sig figs used in the calculation.

6.38 cm x 2.0 cm =12.76 13 cm2 (2 sig figs)

Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft

1.030 g ÷ 2.87 mL 0.358885017 g/mL 0.359 g/mL

Rules for Significant Figures in Mathematical Operations

Addition and Subtraction: The number of decimal places in the answer equals the number of decimal places in the least accurate measurement.

6.8 g + 11.934 g =18.734 18.7 g (3 sig figs)

Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL