Chapter 1Chapter 1Measurements

1.1 Units of Measurement1.1 Units of MeasurementIn chemistry we

•measure quantities.

•do experiments.

•calculate results.

•use numbers to report measurements.

•compare results to standards.

In a measurement•a measuring tool is used to compare some

dimension of an object to a standard.

1.1 Units of Measurement1.1 Units of MeasurementThe metric system or SI (international system)

is

•a decimal system based on 10.

•used in most of the world.

•used everywhere by scientists.

Volume MeasurementVolume Measurement

Volume • is the space occupied by

a substance.

• uses the unit liter (L) in the metric system.

• uses the unit m3 (cubic meter) in the SI system.

• is measured using a graduated cylinder.

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Mass: Amount of matter in an object

Weight: Measures the force with which gravity pulls on an object.

• is measured on a balance.

• uses the unit gram (g) in the metric system.

• uses the unit kilogram (kg) in the SI system.

Measuring MassMeasuring Mass

Temperature MeasurementTemperature Measurement

The temperature of a substance

• indicates how hot or cold it is.

• is measured on the Celsius (C) scale in the metric system.

• on this thermometer is 18 ºC or 64 ºF.

• in the SI system uses the Kelvin (K) scale.

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1.1 Units in the Metric 1.1 Units in the Metric SystemSystem

In the metric and SI systems, one unit is used for each type of measurement:

Measurement Metric SILength meter (m) meter (m)Volume liter (L) cubic meter (m3)Mass gram (g) kilogram (kg)Time second (s) second (s)Temperature Celsius (C) Kelvin (K)

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All other units are derived from these fundamental units

Scientific NotationScientific Notation

Scientific Notation

• is used to write very large or very small numbers.

• for the width of a human hair of 0.000 008 m is written 8 x 10-6 m.

• of a large number such as 4 500 000 s is written 4.5 x 106 s.

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Numbers in Scientific Numbers in Scientific NotationNotation

A number written in scientific notation contains a

• Coefficient (between 0 and 10)• power of 10.

Examples:

coefficient power of ten coefficient power of ten

1.5 x 102 7.35 x 10-4

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Writing Numbers in Writing Numbers in Scientific NotationScientific Notation

To write a number in scientific notation,

• move the decimal point to give a number 1-9.

• show the spaces moved as a power of 10.

Examples: 52 000. = 5.2 x 10 4 0.00178 = 1.78 x

10-3

4 spaces left 3 spaces right

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Comparing Numbers in Comparing Numbers in Standard Standard and Scientific Notationand Scientific NotationHere are some numbers written in standard format

and in scientific notation.

Number in Number in Standard Format Scientific Notation

Diameter of the Earth12 800 000 m 1.28 x

107 m Mass of a typical human

68 kg 6.8 x 101 kg Length of a pox virus

0.000 03 cm 3 x 10-5 cm

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ExamplesExamplesSelect the correct scientific notation for each.

A. 0.000 008 m

1) 8 x 106 m, 2) 8 x 10-6 m,3) 0.8 x 10-

5 m

B. 72 000 g

1) 7.2 x 104 g, 2) 72 x 103 g, 3) 7.2 x 10-4 g

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ExamplesExamples

Write each as a standard number.

A. 2.0 x 10-2 L

1) 200 L, 2) 0.0020 L, 3) 0.020 L

B. 1.8 x 105 g

1) 180 000 g, 2) 0.000 018 g, 3) 18 000 g

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1.4 Accuracy, Precision, and 1.4 Accuracy, Precision, and Significant FiguresSignificant FiguresSignificant figures: The number of

meaningful digits in a measured or calculated quantity. They come from uncertainty in any measurement.

Generally the last digit in a reported measurement is uncertain (estimated).

Exact numbers and relationships (7 days in a week, 30 students in a class, etc.) effectively have an infinite number of significant figures.

Known & Estimated DigitsKnown & Estimated Digits

If the length is reported as 3.26 cm,

• the digits 3 and 2 are certain (known).

• the final digit, 6, is estimated (uncertain).

• all three digits (2, 7, and 6) are significant, including the estimated digit.

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ExamplesExamples

. l8. . . . l . . . . l9. . . . l . . . . l10. . cm

What is the length of the line?

1) 9.2 cm

2) 9.13 cm

3) 9.19 cm

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ExamplesExamplesClassify each of the following as (1) exact or (2)

measurednumbers.

A.__Gold melts at 1064 °C.

B.__1 yard = 3 feet

C.__The diameter of a red blood cell is 6 x 10-4

cm.

D.__There are 6 hats on the shelf.

E.__A can of soda contains 355 mL of soda.

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Accuracy, Precision, and Accuracy, Precision, and Significant FiguresSignificant FiguresRules for counting significant figures (left-to-

right):1. Zeros in the middle of a number are like any

other digit; they are always significant.◦ 4.803 cm 4 sf

2. Rules for counting significant figures (left-to-right):◦ Zero at the beginning of a number are not

significant (placeholders).0.00661 g 3 sf or 6.61 x 10-3 g

Accuracy, Precision, and Accuracy, Precision, and Significant FiguresSignificant FiguresRules for counting significant figures (left-to-

right):3. Zeros at the end of a number and after the

decimal point are always significant.55.220 K 5 sf

4. Zeros at the end of a number and after the decimal point may or may not be significant.34,2000 ? SF

Rounding NumbersRounding Numbers

If the first digit you remove is 4 or less, it and all following digits are dropped from the number

5.664 425 = 5.664 (4 s.f)

If the digit you remove is 5 or greater, the last digit of the number is increases by 1 5.664 525 = 5.665 (4 s.f)

Adding Significant ZerosAdding Significant Zeros Sometimes, a calculator displays a small whole

number. To give an answer with the correct number of significant figures, significant zeros may need to be written after the calculator result.

E.g 8.00 ÷ 2.00 = 4 4.00

3 s.f 3 s.f calculator 2 zeros are needed

result to give 3 s.f

ExamplesExamplesRound off or add zeros to the following

calculated answers to give three significant figures.

A. 824.75 cm

B. 0.112486 g

C. 8.2 L

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ExamplesExamples

State the number of significant figures in each of the following measurements.

A. 0.030 m

B. 4.050 L

C. 0.0008 g

D. 2.80 m

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Multiplication and DivisionMultiplication and Division

When multiplying or dividing

• the final answer must have the same number of significant figures as the measurement with the fewest significant figures.

Example:

110.5 x 0.048 = 5.304 = 5.3 (rounded)

4 SF 2 SF calculator 2 SF

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Addition and SubtractionAddition and Subtraction

When adding or subtracting

• the final answer must have the same number of decimal places as the measurement with the fewest decimal places.

25.2 one decimal place

+ 1.34 two decimal places

26.54 calculated answer

26.5 final answer with one decimal place

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ExamplesExamples

Select the answer with the correct number of significant figures.

A. 2.19 x 4.2 = 1) 9 2) 9.2 3) 9.198

B. 4.311 ÷ 0.07 = 1) 61.59 2) 62 3) 60

C. 2.54 x 0.0028 = 0.0105 x 0.060

1) 11.3 2) 11 3) 0.041

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ExamplesExamples

For each calculation, round off the calculated answer

to give a final answer with the correct number of

significant figures.

A. 235.05 + 19.6 + 2 = 1) 257 2) 256.7 3) 256.65

B. 58.925 - 18.2 =1) 40.725 2) 40.73 3) 40.7

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1.51.5 PrefixesPrefixes

A prefix

in front of a unit increases or decreases the size of that unit.

makes units larger or smaller than the initial unit by one or more factors of 10.

indicates a numerical value.

prefix = value1 kilometer = 1000 meters

1 kilogram = 1000 grams

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Metric and SI PrefixesMetric and SI Prefixes

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ExamplesExamples

Indicate the unit that matches the description.

1. A mass that is 1000 times greater than 1 gram.

1) kilogram 2) milligram 3) megagram

2. A length that is 1/100 of 1 meter.

1) decimeter 2) centimeter 3) millimeter

3. A unit of time that is 1/1000 of a second.

1) nanosecond 2) microsecond 3) millisecond

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