Chapter 1: Measurements

Chapter 1 Goals• Learn the units and abbreviations for the metric (SI)

system• Measured or exact number?• Numbers in scientific notation• Accuracy and precision• Significant figures• The use of prefixes to change base units• Conversion factors• Calculating temperature in Celsius, Fahrenheit, and

Kelvin

Metric (SI) System

• Decimal system based on 10• Used in most of the world (NOT U.S.!)• Used by hospitals and scientists

Know:• Metric (SI) units for length, volume, mass

and temperature

Units of Measurement

Property Metric Unit US Unit Conversion

Length Meter (m) Inch (in) 1m = 39.4 in

1in = 2.54 cm

Volume Liter (L)

Cubic meter (m3)

Quart (qt) 1L = 1.06 qt

1qt = 946 mL

Mass Gram (g)

Kilogram (kg)

Pound (lb) 1kg = 2.20 lb

1lb = 454 g

Temp Celsius (ºC)

Kelvin (K)

Fahrenheit (ºF) 0 ºC, 32ºF, and

273K

* Metric (SI) units in bold

Measured and Exact Numbers

Measured Numbers:• Device• Uncertainty and error

in measurement• An apple is measured

to be roughly 486g on a top loading balance

Exact Numbers:• From definition or

counting items• The number of apples

in a sack is exactly 6• There are exactly 12

inches in a foot

. l . . . . l . . . . l . . . . l . . . . l . . cm

• To measure the length of the red line, we read the markings on the meter stick.

The first digit 2 plus the second digit 2.7

• Estimating the third digit between 2.7–2.8gives a final length reported as

2.75 cm

or 2.76 cm

Measured Numbers

2 3 4

Scientific Notation

• Large Numbers: 12,000,000 = 1.2 x 107

• Small Numbers: 0.00000012 = 1.2 x 10-7

• Short hand: Mass of a proton = 1.67 x 10-27 kg

• Easier to determine magnitude:

0.00000000000000000000000000167 kg

Scientific Notation

• A number in scientific notation contains a coefficient and a power of 10.

coefficient power of ten coefficient power of ten

1.5 x 102 7.35 x 10-4

• Place the decimal point after the first digit. Indicate the spaces moved as a power of ten.

52 000 = 5.2 x 104 0.00378 = 3.78 x 10-3

4 spaces left 3 spaces right

Accuracy and Precision

• Accuracy - close to the actual value

• Precision - repeatability

Example: 3 darts are precise, but not accurate!

Significant Figures

• Significant figures - all the reported numbers including the estimated digit in measured numbers only (not exact)

• All measured values have error• Significant figures are used to track digits of

importance through calculations• Good explanation of sig figs is given on page 10

(table 1.3)

Counting Sig Figs1. All non-zero digits are significant2. Zeroes may or may not be significant

Significant:• Sandwiched between two non-zero digits

(607 m or 3.062 in)• At the end of a decimal (80. L or 65.0 ºC)• Any digit in the coefficient of a number in sci. not.

(5.50 x 103 m or 4.00 x 10-2 g)Not significant:• At the beginning of a decimal number (small number)

(0.0005 m or 0.015 g)• Used as a place holder for a large number without a decimal

(530,000 m2 or 1,250,000 g)

Examples

Significant figures?

a.) 8.00 x 102 m

b.) 0.00002 L

c.) 600. in

d.) 20.60 mL

e.) 54,000 cm

Examples

Significant figures?

a.) 8.00 x 102 m - 3 sig figs

b.) 0.00002 L - 1 sig fig

c.) 600. In - 3 sig figs

d.) 20.60 mL - 4 sig figs

e.) 54,000 cm - 2 sig figs

Examples

Scientific notation?

a.) 60,800,000 sec (4sig figs)

b.) 0.00820 ft (2 sig figs)

c.) 0.00000345 L (3 sig figs)

d.) 2600 mL (3 sig figs)

Examples

Scientific notation?

a.) 60,800,000 sec (4 sig figs) - 6.080 x 107 sec

b.) 0.00820 ft (2 sig figs) - 8.2 x 10-3 ft

c.) 0.00000345 L (3 sig figs) - 3.45 x 10-6 L

d.) 2600 mL (3 sig figs) - 2.60 x 103 mL

Sig Figs in Calculations• Rounding off:

– If first digit dropped is 4 or less the number is rounded down. If it is 5 or more the number is rounded up

8.4234 8.42 (3 sig figs) or 8.4 (2 sig figs)14.780 14.8 (3 sig figs) or 15 (2 sig figs)

• Multiplication and Division:– The number with the lesser amount of sig figs determines the sig

figs in the answer

34.6 x 0.54 = 0.27804 0.28 (rounded to 2 sig figs) 67.2

Sig Figs in Calculations

• Addition and Subtraction:

– The number with the lesser amount of decimal places is used to determine decimal places in the answer

5.048 + 45.1 = 50.148 50.1 (1 decimal place)

Metric and SI System Prefixes

Prefix Abbreviation Conversion

Mega M 1,000,000

Kilo k 1,000

-- -- 1

Centi c 1/100

Milli m 1/1,000

Micro µ 1/1,000,000

Metric and SI System Prefixes

1000g = 1 kilogram (kg) or 1g = 0.001kg

1m = 100centimeter (cm) or 0.01m = 1cm

1L = 1000milliliters (mL) or 0.001L = 1mL

Volume and Converting Cubic Units

• 1000 mL = 1 L

• 1 mL = 1 cm3 = 1 cc

• 100 cm = 1 m

• 100 cm3 IS NOT = 1 m3

• (1m)3 = (100 cm)3 = 1,000,000 cm3

Conversion Factors

• Used for converting units and used A LOT in chemistry!

• Step 1 – Identify information given• Step 2 – Plan how to reach desired units• Step 3 – Select necessary conversion factors• Step 4 – Set up conversions so they cancel• Step 5 – Solve problem and determine sig figs*• Unit should cancel leaving you with desired units

Example

During surgery, a patient receives 5.0 pints of plasma. How many milliliters of plasma were given? 1 quart = 2pints

Examplestep 1: Given 5.0 pints

step 2: pints quarts milliliters

step 3: 1 quart = 2pints and

1 quart = 946mL and

step 4:

1quart

2 p int s

2 p int s

1quart

1quart

946mL

946mL

1quart

5.0 p int s 1quart

2 p int s

946mL

1quart[2365] 2400mL

Density

• The relationship between mass and volume

• Density can be used as a conversion factor

• Specific gravity is unitless but roughly equal to density numerically

Volume

MassDensity

erDensityWat

erialDensityMatavitySpecificGr

Temperature

• Measures how hot or cold things are

• Measure in Fahrenheit, Celcius and Kelvin scales

• Can NOT be converted simply using conversion factors

• Different freezing temps for each scale

32)(8.1 CF

8.1

)32(

FC

C K 273

K o C 273