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Chapter 1

Measurement

F. Morales

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CHAPTER OUTLINE

Scientific Method Measurements/SI Units Volume & Density Conversion of Units Scientific Notation Significant Figures

The Nature of Science—Scientific Method

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- Science is NOT a body of knowledge, but a method to understand nature & how it works

- Science accepts nothing on faith- The ultimate judge is always the experiment

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SCIENTIFICMETHOD

The scientific method is a process of creative thinking and testing aimed at objective and verifiable discoveries.

Knowledge gained through the scientific method is self-correcting and improves over time.

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MEASUREMENTSSI UNITS

Measurements are made by scientists to determine size, length and other properties of matter.

For measurements to be useful, a measurement standard must be used.

A standard is an exact quantity that people agree to use for comparison.

SI is the standard system of measurement used worldwide by scientists.

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SI BASE UNITS

Quantity Measured Units Symbol

Length Meter m

Mass Kilogram kg

Time Seconds s

Temperature Kelvin K

Electric current Ampere A

Amount of substance Mole mol

Intensity of light Candela cd

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DERIVED UNITS

Quantity Measured Units Symbol

Volume Liter L

Density grams/cc g/cm3

In addition to the base units, several derived units are commonly used in SI system.

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VOLUME

Volume is the amount of space an object occupies.

Common units are cm3 or liter (L) and milliliter (mL).

1 L = 1000 mL 1 mL = 1 cm3

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DENSITY

Density is mass per unit volume of a material. Common units are g/cm3 (solids) or g/mL (liquids).

Which has greatest density?

Density is directly related to the mass of an object.

Density is indirectly related to the volume of an object.

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CONVERSIONOF UNITS

The SI system of units is easy to use because it is based on multiples of ten.

Common prefixes are used with the base units to indicate the multiple of ten that the unit represents.

Prefixes Symbol Multiplying factor

mega- M 1,000,000

kilo- k 1000

centi- c 0.01

milli- m 0.001

micro- 0.000,001

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CONVERSIONOF UNITS

How many mm are in a cm? 10How many cm are in a km? 10x10x10x10x10100000 or 105

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CONVERSIONOF UNITS

Any unit can be converted into another by use of the appropriate conversion factor.

beginning unit x = final unit

beginning unit

final unit

Conversion factor

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Example 1:

The length of a football field is 100 yards. What is the length of the field in meters? (1m = 1.094 yd)

91.4 m100 yd m

x = yd

11.094

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Example 2:

25 mm2.5 cm mm

x = cm

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The thickness of a book is 2.5 cm. What is this measurement in mm?

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Example 3:

How many centimeters are in 2.0 ft? (1 in = 2.54 cm)

inx

ft 112 cm

x = in

61 cm2.0 ft2.54

1

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Example 4:

How many seconds are there in 1 day?

hrx

day 124 min

x hr

= 86400 s

1 day60

1

s x

min 601

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Example 5:

If the density of gold is 19.3 g/cm3, how many grams does a 5.00 cm3 nugget weigh?

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g x =

cm 5.00 cm3

19.396.5 g

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Example 6:

mL x =

g 60.0 g

13.64.41 mL

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What volume of mercury has a mass of 60.0 g if its density is 13.6 g/mL?

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IS UNIT CONVERSIONIMPORTANT?

In 1999 Mars Climate orbiter was lost in space because engineers failed to make a simple conversion from English units to metric, an embarrassing lapse that sent the $125 million craft fatally close to the Martian surface.

Further investigation showed that engineers at Lockheed Martin, which built the aircraft, calculated navigational measurements in English units. When NASA’s JPL engineers received the data, they assumed the information was in metric units, causing the confusion.

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SCIENCTIFICNOTATION

Scientific Notation is a convenient way to express very large or very small quantities.

Its general form is

A x 10n

coefficient

1 < A < 10

n = integer

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SCIENTIFICNOTATION

To convert from decimal to scientific notation: Move the decimal point so that it’s located after the first

nonzero digit. Follow the new number by a multiplication sign and 10

with an exponent (power). The exponent is equal to the number of places that the

decimal point was shifted.

7 5 0 0 0 0 0 0

7.5 x 10 7

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SCIENTIFICNOTATION

For numbers smaller than 1, the decimal moves to the left and the power becomes negative.

0 0 0 6 4 2

6.42 x 103

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Write 6419 in scientific notation.

6419.6.419 x 103

decimal after first nonzero

digitpower of 10

Example 1:

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Write 0.000654 in scientific notation.

0.0006546.54 x 10-4

decimal after first nonzero

digit

power of 10

Example 2:

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CALCULATIONS WITHSCIENTIFIC NOTATION

To perform multiplication or division with scientific notation:

1. Change numbers to exponential form.

2. Multiply or divide coefficients.

3. Add exponents if multiplying, or subtract exponents if dividing.

4. If needed, reconstruct answer in standard exponential form.

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Multiply 30,000 by 600,000

Example 1:

Convert to exponential form

(3 x 104) (6 x 105) =

Multiply coefficients

18 x 10

Add exponents

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Reconstruct answer

1.8 x 1010

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Divide 30,000 by 0.006

Example 2:

Convert to exponential form

(3 x 104) / (6 x 10-3) =

Divide coefficients

= 0.5 x 10

Subtract exponents

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Reconstruct answer

5 x 106

(3 x 104) (6 x 10-3) = x 104-(-3) 3

6

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SIGNIFICANTFIGURES

Two kinds of numbers are used in science:

Counted or defined:

exact numbers; have no uncertainty

Measured:

are subject to error; have uncertainty

Every measurement has uncertainty because of instrument limitations and human error.

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UNCERTAINTY IN MEASUREMENTS

What is this measurement?

8.65certain uncertain

What is this measurement?

8.6certain uncertain

The last digit in any measurement is the estimated one.

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SIGNIFICANTFIGURES RULES

Significant figures are the certain and uncertain digits in a measurement.1. All non-zero digits are significant.

2. All sandwiched zeros are significant.

3. Leading zeros (before or after a decimal) are NOT significant.

4. Trailing zeros (after a decimal) are significant.

0 . 0 0 4 0 0 4 5 0 0

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Examples:

Determine the number of significant figures in each of the following measurements:

461 cm 3 sig figs

1025 g 4 sig figs

0.705 mL 3 sig figs

93.500 g 5 sig figs

0.006 m 1 sig fig

5500 km 2 sig figs

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ROUNDING OFFNUMBERS

If rounded digit is less than 5, the digit is dropped.

51.234 Round to 3 sig figs

Less than 51.875377 Round to 4 sig figs

Less than 5

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ROUNDING OFFNUMBERS

If rounded digit is equal to or more than 5, the digit is increased by 1.

51.369 Round to 3 sig figs

More than 5

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5.4505 Round to 4 sig figs

Equal to 5

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51.369

5.4505

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SIGNIFICANTFIGURES & CALCULATIONS

The results of a calculation cannot be more precise than the least precise measurement.

In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.

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(9.2)(6.80)(0.3744) = 23.4225

Calculator answer

3 sig figs 4 sig figs

The answer should have two significant figures because 9.2 is the number with the fewest significant figures.

The correct answer is 23

2 sig figs

MULTIPLICATION& DIVISION

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SIGNIFICANTFIGURES & CALCULATIONS

The results of an addition or a subtraction must be expressed to the same precision as the least precise measurement.

The result must be rounded to the same number of decimal places as the value with the fewest decimal places.

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Add 83.5 and 23.28

83.523.28

106.78Calculator

answer

Least precise number

106.8Correct answer

ADDITION &SUBTRACTION

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Example 1:

5.008 + 16.2 + 13.48 = 34.688

Least precise number

Round to

7

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Example 2:

3.15 x 1.53=

0.786.1788

2 sig figs

3 sig figs

Round to

2

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THE END