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THE NUMERICAL SIDE OF PHYSICS

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Objectives

1. Determine the number of significant figures in a numerical value.

2. Convert a number from normal notation to scientific notation

3. Use unit analysis to convert a measurement to another set of units

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Significant Figures

• the number of meaningful digits in a measured or calculated quantity

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Guidelines for UsingSignificant Figures

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Any digit that is not zero

is significant

Example: 845 cm has 3 SFs

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Zeros between nonzero digits

are significant

Example: 40,501 kg contains 5 SFs

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Zeros to the left of the first

nonzero digit are

not significant

Example: 0.008 L contains 1 SF

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If the number is >1, then all

the zeros written to the right

of the decimal point is

significant

Example: 2.00 mg has 3 SFs

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If a number is <1, the zeros

that are at the end of the

number and the zeros that are

between nonzero digits are

significant

Examples: 0.090 kg has 2 SFs

0.0405 g has 3 SFs

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For numbers that do not contain

decimal points, the trailing zeros

(that is, zeros after the last

nonzero digit) may or may not

be significant

Example: 400 can be expressed as

4 x 102 for 1 SF

4.0 x 102 for 2 SFs

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Rounding Off

A number is rounded off to the

desired number of significant

figures by dropping one or more

digits to the right

42510011 0010 1010 1101 0001 0100 1011

Rounding Off Rules

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When the first digit dropped

is <5, the last digit retained

should remain unchanged

Example: 4.13 can be rounded off to 4.1

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0011 0010 1010 1101 0001 0100 1011When it is >5, 1 is added to the

last digit retained

Example:

4.17 can be rounded off to 4.2

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When it is exactly 5, 1 is added

to the last digit retained if

that digit is odd,

but remains as is when

it is even

Examples: 4.15 can be rounded off to 4.2

4.45 can be rounded off to 4.4

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In chain calculations, only

the final answer is rounded

off to the correct number of

significant figures

42510011 0010 1010 1101 0001 0100 1011

Addition and Subtraction

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In addition and subtraction,

the answer cannot have more

digits to the right of the

decimal point than either of the

original numbers

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Example 89.332

+ 1.1

90.432

one digit after the decimal pt.

round off to 90.4

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Multiplicationand Division

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In multiplication and division,

the number of significant figures

in the final product or quotient is

determined by the original

number that has the smallest

number of significant figures

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Examples:

2.8 x 4.5039 =

12.61092 round off to 13

6.85/112.04 =

0.0611388789 round off to 0.0611

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Scientific Notation

used when working with very large and

very small numbers

expressed in the form:

N x 10n

where N- number between 1 and 10

n- exponent, + or - integer

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If the decimal point

has to be moved:

to the left n is +

to the right n is -

Examples:

568.762 = 5.68762 x 102 n = 2

0.00000772 = 7.72 x 10-6 n = - 6

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Addition and Subtraction

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• To add or subtract using scientific notation, write each quantity, say N1 and N2 -with the same exponent n then combine N1 and N2 the exponents remain the same

Example:

(7.4 x 103) + (2.1 x 103) = 9.5 x 103

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Multiplicationand Division

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• To multiply numbers expressed in scientific notation, we multiply N1 and N2 and then add the exponents together

Example:

(8.0 x 104) x (5.0 x 102)

= (8.0 x 5.0)( 104+2) = 40 x 106

= 4.0 x 107

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To divide using scientific

notation, we divide

N1 and N2 and then subtract

the exponents

Example:

(6.9 x 107)/(3.0 x 10-5) = (6.9/3.0) x 107-(-5)

= 2.3 x 1012

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Unit Conversions

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Base Quantity Name of Unit Symbol

Length meter m

Mass kilogram kg

Time second s

Electrical current ampere A

Temperature kelvin K

Amount of substance mole mol

Luminous intensity candela cd

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Prefixes used with SI Units

Prefix Symbol Meaning Example

Tera- T 1012 1 terameter (Tm) = 1 x 1012 m

Giga- G 109 1 gigameter (Gm) = 1 x 109 m

Mega- M 106 1 megameter (Mm) = 1 x 106 m

Kilo- k 103 1 kilometer (km) = 1 x 103 m

Deci- d 10-1 1 decimeter (dm) = 0.1 m

Centi- c 10-2 1 centimeter (cm) = 0.01 m

Milli- m 10-3 1 millimeter (mm) = 0.001 m

Micro- μ 10-6 1 micrometer (μm) = 1 x 10-6 m

Nano- n 10-9 1 nanometer (nm) = 1 x 10-9 m

Pico- p 10-12 1 picometer (pm) = 1 x 10-12 m

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Unit Conversion Factors

LENGTH

1 m = 100 cm = 1000 mm = 106 μm = 109 nm

1 km = 1000 m = 0.6214 mi

1 in = 2.540 cm

1 ft = 30.48 cm

1 yd = 91.44 cm

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TIME

1 min = 60 s

1 h = 3600 s

1 d = 86,400 s

1 y = 365.24 d = 3.156 x 107 s

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MASS

1 kg = 103 g = 2.205 lb

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VOLUME

1 liter= 1000 mL = 1000 cm3 = 1 dm3 = 10-3 m3

1 ft3 = 0.02832 m3 = 28.32 liters = 7.477 gallons

1 gallon = 3.788 liters

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Simple Conversion

Convert 22 inches into feet

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Answer

• 22 in x (1 ft/12 in) = 1.8 ft

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Multiple Conversion

Convert 2,700 mL into gallon

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Answer

2700 mL x (1 L/1000 mL) x (1 gal/3.788 L)

= 0.7128 gal

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Determine the number of SFs of the following measurements

1. 478 cm 6. 0.043 kg2. 6.01 g 7. 560 mg3. 0.825 m 8. 453.2 cm4. 3001 km 9. 2.60 dm5. 1,020 mL 10. 200 L

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Perform the operations and express the answers to the correct number of SFs

1. 11,254.1 g + 0.1983 g 2. 0.0154 kg / 88.3 mL3. 66.59 L – 3.113 L 4. 2.64 x 103 cm + 3.27 x 102 cm5. 8.16 m x 5.1355 m

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Express the ff. numbers in scientific notation1. 0.000000027

2. 0.096

3. 356

4. 602,200,000,000,000,000,000,000

5. 0.00000000000000000000000166

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1.A person’s average daily intake of glucose (a form of sugar) is 0.0833 pound (lb). What is this mass in milligrams?

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2.An average adult has 5.2 L of blood. What is the volume of blood in m3?