Chapter 1.3: Measurement

Measurements and Their Uncertainty The International System of Units Density Temperature

Scientific Notation

“Writing a number as a power of 10.”

Why? It makes very large and very small numbers more manageable to write and use.– Rule of thumb: Use when number is greater than 10

or smaller than 0.1 Or, you may always use it!

The number of sig. figs are clearly shown in a measurement.

Scientific Notation

How important is a change in the power of 10?

Diameter of Earth’s orbit around the sun≈ 100,000,000,000 m = 1.0*1011 m

Diameter of an atom

≈ 0.0000000001 = 1.0*10-10 m

1. Move the decimal point in the original number so that it is located to the right of the first nonzero digit.

2. Multiply the new number by 10 raised to the proper power that is equal to the number of places the decimal moved.

3. If the decimal point moves: To the left, the power of 10 is positive. To the right, the power of 10 is negative.

Writing in scientific notation

Significant figures (“sig figs”): the digits in a measurement that are reliable (or precise). The greater the number of sig figs, the more precise that measurement is.

A more precise instrument will give more sig figs in its measurements.

Significant Figures

Every measurement has some degree of uncertainty.

“PACIFIC”

Decimal point is PRESENT. Count digits from left side, starting with the first nonzero digit.

40603.23 ft2

0.01586 mL

= 7 sig figs

= 4 sig figs

PACIFIC

PACIFIC

The “Atlantic-Pacific” Rule

When are digits “significant”?

“ATLANTIC”

Decimal point is ABSENT. Count digits from right

side, starting with the first

nonzero digit.

40600 ft2

1000 mL

3 sig figs =

1 sig fig =

ATLANTIC

ATLANTIC

0.00932Decimal point present → “Pacific” → count digits from left,

starting with first nonzero digit= 3 sig figs

4035Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit= 4 sig figs

27510Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit= 4 sig figs

Examples

Sig. Figs. In Calculations And Scientific Notation

In this class, use scientific notation for all numbers greater than 10 and smaller than 0.1 and write all calculations to the correct number of significant figures

• In this class, we WILL follow the sig. fig. rules for operations

Write the following measurements in scientific notation, then record the number of sig figs.

1. 789 g

2. 96,875 mL

3. 0.0000133 J

4. 8.915 atm

5. 0.94°C

7.89*102 g9.6875*104 mL

1.33*10-5 J8.915 atm9.4*10-1 °C

3 sig figs5 sig figs3 sig figs4 sig figs2 sig figs

Practice problems

Accuracy & Precision

Precision: How closely individual measurements agree

with each other The “fineness” of a measurement

Accuracy: how closely individual measurements agree with the true or accepted value

Accurate or Precise?

Precise!(but not accurate)

What is the temperature at which water boils?

•Measurements: 95.0°C, 95.1°C, 95.3°C

•True value: 100°C

Accurate or Precise?

Accurate!(it’s hard to be accurate without being precise)

What is the temperature at which water freezes?

•Measurements: 1.0°C, 1.2°C, -5.0°C

•True value: 0.0°C

Accurate or Precise?

Not Accurate & Not Precise(don’t quit your day job)

What is the atmospheric pressure at sea level?

•Measurements: 10.01 atm, 0.25 atm, 234.5 atm

•True value: 1.00 atm

Accurate or Precise?

Accurate & Precise(it’s time to go pro)

What is the mass of one Liter of water?

•Measurements: 1.000 kg, 0.999 kg, 1.002 kg

•True value: 1.000 kg

A graduated cylinder:

50

100 mL Beaker

50 mL Graduated cylinder

A beaker:

41.0

41.2 mL (3 sig figs = very precise)

40. mL (2 sig figs = not as precise)

Precision examples: To measure the time for a pencil to fall…

compare a stopwatch and a wall clock. To measure the volume of a liquid…

compare a graduated cylinder and a beaker.

The stopwatch & graduated cylinder are more precise instruments…so the readings

they produce will have more sig figs.

The Metric System – SI Units of Measurement

History of S.I. The Prefixes The Base Units Length, Volume, Mass,

Temperature, Density and Temperature

International System of Units

Why was it organized? It is simple, being based on powers of 10. (like our number system)

Every country in the world uses the metric system except the USA, Myanmar, and Liberia.

By 2009, all products sold in Europe must use the metric system. No dual-labelling will be permitted.

Visit U.S. Metric Association (USMA), Inc. for more info.

International System of Units

Scientists use a set of measuring units called SI, or the International System of Units.

Metric Prefixes

Metric Prefixes (pg. 17 Memorize) A metric prefix indicates how many times a unit

should be multiplied or divided by 10. Sometimes units have to be converted to other

units (grams to kilograms)

The Metric Prefixes

Prefix Symbol Value Power Use

mega M 1,000,000 106 megaton

kilo k 1,000 103 kilometer

deci d 0.1 10-1 decimate

centi c 0.01 10-2 centipede

milli m 0.001 10-3 millimeter

micro 0.000001 10-6 microscope

nano n 0.000000001 10-9 nanotechnology

giga G 1,000,000,000 109 gigabyte

Derived Units

Additional SI units, including volume and density, are called derived units.

Derived units are made from combinations of base units.

Derived Units

Combination of base units. Volume= length width height

1 cm3 = 1 mL Density - mass per unit volume (g/cm3)

D = MV D

M

V

Density

An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

M = ?

WORK:

M = DV

M = (13.6 g/cm3)(825cm3)

M = 11,220 g

DM

V

Density

A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

M = 25 g

DM

V

WORK:

V = M D

V = 25 g

0.87 g/mL

V = 28.7 mL

Density

You have a sample with a mass of 620 g & a volume of 753 cm3. Find density.

GIVEN:

M = 620 g

V = 753 cm3

D = ?

DM

V

WORK:

D = M V

D = 620 g

753 cm3

D = 0.82 g/cm3

Measuring Temperature

Temp.- a measure of how hot or how cold something is [*Base unit is Kelvin (K)]

Thermometer used to measure 2 most familiar scales: Celsius and Fahrenheit

(Fahrenheit is not used in science) Water Boils: 100oC; 212oF Water Freezes: 0oC; 32oF

Measuring Temperature

Temperature can be converted from Fahrenheit to Celsius to Kelvins.

To convert:K = °C + 273.15°F = (1.8 * °C) + 32°C = (°F-32) 1.8

**Fahrenheit cannot be converted directly to Kelvins.

0 Kelvin-lowest possible temp that can be reached; 0K= -273.15oC (ie. Absolute zero)